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Functions (Cambridge (CIE) IGCSE Maths: Extended)

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1
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straight f left parenthesis x right parenthesis space equals space 3 x space – space 5

The domain of straight f left parenthesis x right parenthesis is open curly brackets – 3 comma 0 comma 2 close curly brackets.

Find the range of straight f left parenthesis x right parenthesis.

{ ........................................... } [2]

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2a
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straight f open parentheses x close parentheses equals 7 x minus 4      straight g open parentheses x close parentheses equals fraction numerator 2 x over denominator x minus 3 end fraction comma space x not equal to 3   straight h open parentheses x close parentheses equals x squared

Find space straight g open parentheses 6 close parentheses.

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2b
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Find space fg open parentheses 4 close parentheses.

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2c
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Find space fh open parentheses x close parentheses.

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3
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straight f left parenthesis x right parenthesis equals 7 minus 2 x space space space space space space space space space space space space space space space straight g left parenthesis x right parenthesis equals 10 over x comma space x not equal to 0 space space space space space space space space space space space space space space space straight h left parenthesis x right parenthesis equals 27 to the power of x

Find

i) straight f left parenthesis negative 3 right parenthesis,

 

[1]

ii) hg left parenthesis 30 right parenthesis,

 

[2]

iii) straight f to the power of negative 1 end exponent left parenthesis x right parenthesis.

 

straight f to the power of negative 1 end exponent left parenthesis x right parenthesis equals................................................... [2]

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4a
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straight f left parenthesis x right parenthesis equals fraction numerator 3 over denominator x plus 2 end fraction comma space x not equal to negative 2         straight g left parenthesis x right parenthesis equals 8 x minus 5         

Work out space straight g open parentheses 1 fourth close parentheses.

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4b
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Work out space ff left parenthesis 2 right parenthesis.

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4c
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Find space gg left parenthesis x right parenthesis, giving your answer in its simplest form.

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4d
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Find space straight g to the power of negative 1 end exponent left parenthesis x right parenthesis.  

straight g to the power of negative 1 end exponent left parenthesis x right parenthesis equals..................................................

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5a
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straight f and straight g are functions such that

               straight f open parentheses x close parentheses space equals space 2 over x squared space space space space space space space space space space and space space space space space space straight g open parentheses x close parentheses space equals space 4 x cubed

Find straight f left parenthesis negative 5 right parenthesis

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5b
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Find fg open parentheses 1 close parentheses.

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1a
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space space space space space space space space space space straight g open parentheses x close parentheses space equals space 1 minus space 2 x space space space space space space space space space space space straight h open parentheses x close parentheses space equals space 1 over x comma space x space not equal to 0 space space space space space space space space space space straight j open parentheses x close parentheses space equals space 5 to the power of x

 

Find hh left parenthesis x right parenthesis, giving your answer in its simplest form.

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1b
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Find straight j open parentheses 5 close parentheses.

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1c
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Find the value of x.

x space equals ................................................ 

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2a
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straight f open parentheses x close parentheses equals 3 x plus 2      straight g open parentheses x close parentheses equals x squared plus 1      straight h open parentheses x close parentheses equals 4 to the power of x

Find space straight h open parentheses 4 close parentheses.

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2b
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Find space fg open parentheses 1 close parentheses.

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2c
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Find space gf open parentheses x close parentheses in the form space a x squared plus b x plus c.

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2d
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Find x when space straight f open parentheses x close parentheses equals straight g open parentheses 7 close parentheses.  

x equals................................................ 

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2e
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Find space straight f to the power of negative 1 end exponent open parentheses x close parentheses.  

straight f to the power of negative 1 end exponent open parentheses x close parentheses equals................................................ 

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3a
Sme Calculator2 marks

space straight f left parenthesis x right parenthesis equals 4 x minus 1        space straight g left parenthesis x right parenthesis equals x squared        space straight h left parenthesis x right parenthesis equals 3 to the power of negative x end exponent

Find in its simplest form

i)space straight f left parenthesis x minus 3 right parenthesis,

[1]

ii)space straight g left parenthesis 5 x right parenthesis.

[1]

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3b
Sme Calculator2 marks

Findspace straight f to the power of negative 1 end exponent left parenthesis x right parenthesis.

space straight f to the power of negative 1 end exponent left parenthesis x right parenthesis equals ................................................. 

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3c
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Find the value ofspace hh left parenthesis 1 right parenthesis, correct to 4 significant figures.

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4
Sme Calculator7 marks

straight g left parenthesis x right parenthesis equals 8 x minus 5 space space space space space space space space space space space space space space straight h left parenthesis x right parenthesis equals x squared plus 6

i) Show that space hg left parenthesis x right parenthesis equals 19 space simplifies to space 16 x squared minus 20 x plus 3 equals 0.  

[3]

ii) Use the quadratic formula to solve space 16 x squared minus 20 x plus 3 equals 0.
Show all your working and give your answers correct to 2 decimal places.  

x equals......................... or x equals......................... [4]

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1
Sme Calculator1 mark

straight h open parentheses x close parentheses equals 4 to the power of x.

Find x when space straight h to the power of negative 1 end exponent open parentheses x close parentheses equals 2.  

x equals................................................ 

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2a
Sme Calculator2 marks

space straight f left parenthesis x right parenthesis equals 4 x minus 1        space straight g left parenthesis x right parenthesis equals x squared        space straight h left parenthesis x right parenthesis equals 3 to the power of negative x end exponent

Show thatspace straight g left parenthesis 3 x minus 2 right parenthesis minus straight h left parenthesis negative 3 right parenthesis can be written as 9 x squared minus 12 x minus 23.

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2b
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Find x whenspace straight f left parenthesis 61 right parenthesis equals straight h left parenthesis x right parenthesis.

x equals ................................................. 

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3a
Sme Calculator1 mark

straight h left parenthesis x right parenthesis space equals space 2 to the power of x

Solve the equation space h to the power of negative 1 end exponent left parenthesis x right parenthesis space equals space 0.5.

x space equals .............................................. 

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3b
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fraction numerator 1 over denominator straight h left parenthesis x right parenthesis end fraction space equals space 2 to the power of k x end exponent Write down the value of k.

k space equals .............................................. 

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4
Sme Calculator3 marks

straight h left parenthesis x right parenthesis equals x to the power of x comma space x greater than 0

i) Calculate straight h left parenthesis 0.3 right parenthesis. Give your answer correct to 2 decimal places.

[2]

ii) Find x when straight h left parenthesis x right parenthesis equals 256.

x equals............................................... [1]

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