Functions (Edexcel IGCSE Maths A)

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Cards in this collection (23)

  • What is a function?

    A function is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers.

  • What do the notations  straight f open parentheses x close parentheses equals...  or  straight f colon x rightwards arrow from bar...  indicate?

    The notations  straight f open parentheses x close parentheses equals...  or  straight f colon x rightwards arrow from bar...  indicate a function straight f, where x is the input and straight f open parentheses x close parentheses is the output.

    You should be familiar with both notations, as either one can appear on the exam.

  • What is the input of a function?

    The input of a function is the number being put into the function, often referred to as  x.

  • What is the output of a function?

    The output of a function is the number coming out of the function, often referred to as straight f open parentheses x close parentheses or y.

  • How would you find the value of straight f open parentheses 3 close parentheses for a function straight f open parentheses x close parentheses?

    To find the value of straight f open parentheses 3 close parentheses for a function straight f open parentheses x close parentheses, substitute x equals 3 into the equation of the function.

    For example, if straight f left parenthesis x right parenthesis equals 2 x plus 1, then straight f left parenthesis 3 right parenthesis equals 2 open parentheses 3 close parentheses plus 1 equals 6 plus 1 equals 7.

  • How would you find the value of x if you knew that straight f open parentheses x close parentheses equals 15?

    To find the value of x if you know that straight f open parentheses x close parentheses equals 15:

    • Set the equation for straight f open parentheses x close parentheses equal to 15

    • Then solve for x

    For example, if straight f open parentheses x close parentheses equals 2 x plus 1 and straight f open parentheses x close parentheses equals 15, then

    2 x plus 1 equals 15 space space space rightwards double arrow space space space 2 x equals 14 space space space rightwards double arrow space space space x equals 7

  • Define the domain of a function.

    The domain of a function is the set of all inputs that are allowed to be put into the function.

  • True or False?

    The domain of straight f open parentheses x close parentheses equals 1 over x is "all values of x".

    False.

    straight f open parentheses x close parentheses equals 1 over x is not defined when x equals 0.

    Therefore zero must be excluded from the domain of straight f open parentheses x close parentheses.

    straight f open parentheses x close parentheses equals 1 over x, x not equal to 0.

  • Define the range of a function.

    The range of a function is the set of all outputs that the function gives out, based on the set of all inputs (the range) that can be put in.

  • True or false?

    The function straight f open parentheses x close parentheses equals x squared with domain "all values of x" also has a range which is "all values of x".

    False.

    Whether x is positive or negative, straight f open parentheses x close parentheses equals x squared can only ever be positive or zero.

    The domain is 'all values of x' and the range is straight f open parentheses x close parentheses greater or equal than 0.

  • Out of the domain and range of a function, which one is expressed in terms of x, and which one is expressed in terms of y or straight f open parentheses x close parentheses?

    The domain is expressed in terms of x (e.g.  x not equal to 0).

    The range is expressed in terms of y or straight f open parentheses x close parentheses  (e.g.  y greater or equal than 0  or  straight f open parentheses x close parentheses greater or equal than 0 ).

  • Define a composite function.

    A composite function is a function that 'combines' two functions.

    The output of one function is used as the input for the other function.

  • What does the notation fg open parentheses x close parentheses mean?

    fg open parentheses x close parentheses is the notation for a composite function made up of functions straight f and straight g.

    It means "straight f is applied to the output of straight g open parentheses x close parentheses".

    I.e., first put x into the function straight g, and next put the output straight g open parentheses x close parentheses into the function straight f.

    Note that the function on the right (straight g) acts first, and the function on the left (straight f) acts second.

  • What does the notation gf open parentheses x close parentheses mean?

    gf open parentheses x close parentheses is the notation for a composite function made up of functions straight g and straight f.

    It means "straight g is applied to the output of straight f open parentheses x close parentheses".

    I.e., first put x into the function straight f, and next put the output straight f open parentheses x close parentheses into the function straight g.

    Note that the function on the right (straight f) acts first, and the function on the left (straight g) acts second.

  • How would you find the value of fg open parentheses 2 close parentheses?

    To find the value of fg open parentheses 2 close parentheses:

    1. First substitute x equals 2 into the equation for straight g open parentheses x close parentheses.

    2. Then substitute the output straight g open parentheses 2 close parentheses into the equation for straight f open parentheses x close parentheses.

  • Give the definition of an inverse function.

    An inverse function is a function that does the exact opposite operations of the function it came from.

  • What is the notation for the inverse function of the function straight f open parentheses x close parentheses?

    The notation for the inverse function of the function straight f open parentheses x close parentheses is straight f to the power of negative 1 end exponent open parentheses x close parentheses.

  • What are the steps to find the inverse function straight f to the power of negative 1 end exponent open parentheses x close parentheses of straight f open parentheses x close parentheses?

    To find straight f to the power of negative 1 end exponent open parentheses x close parentheses:

    1. Write straight f open parentheses x close parentheses as y italic equals open parentheses formula space in italic space x close parentheses.

    2. Swap x and y to get x italic equals open parentheses formula space in italic space y close parentheses.

    3. Rearrange to make y the subject.

    4. Replace y with straight f to the power of negative 1 end exponent open parentheses x close parenthesesto rewrite as straight f to the power of negative 1 end exponent open parentheses x close parentheses equals....

  • If you knew that straight f open parentheses 3 close parentheses equals 10, how would you find straight f to the power of negative 1 end exponent open parentheses 10 close parentheses?

    An inverse function 'undoes' the operations of the original function.

    So if straight f turns 3 into 10, then straight f to the power of negative 1 end exponent turns 10 back into 3.

    I.e., if straight f open parentheses 3 close parentheses equals 10, then straight f to the power of negative 1 end exponent open parentheses 10 close parentheses equals 3.

  • What is ff to the power of negative 1 end exponent open parentheses x close parentheses equal to?

    ff to the power of negative 1 end exponent open parentheses x close parentheses is a composite function of straight f and its inverse straight f to the power of negative 1 end exponent.

    An inverse function 'undoes' the operations of the original function (and vice versa).

    So ff to the power of negative 1 end exponent open parentheses x close parentheses equals x.

    (Note that straight f to the power of negative 1 end exponent straight f open parentheses x close parentheses equals x as well.)

  • What is the domain of straight f to the power of negative 1 end exponent open parentheses x close parentheses?

    The domain of straight f to the power of negative 1 end exponent open parentheses x close parentheses has the same values as the range of straight f open parentheses x close parentheses.

    When writing down this domain, you must write it in terms of x.

  • What is the range of straight f to the power of negative 1 end exponent open parentheses x close parentheses?

    The range of straight f to the power of negative 1 end exponent open parentheses x close parentheses has the same values as the domain of straight f open parentheses x close parentheses.

    When writing down the range of straight f to the power of negative 1 end exponent open parentheses x close parentheses, use straight f to the power of negative 1 end exponent open parentheses x close parentheses as the variable, not x.

  • True or false?

    Completing the square can help find inverse functions.

    True.

    Completing the square can help rearrange a quadratic expression in order to find its inverse function.