Functions (Cambridge (CIE) O Level Additional Maths): Exam Questions

It is given that , where  and  are non-zero constants.

(i) Explain why  is not a suitable domain for .

(ii) Given that  and  , find the values of  and .

Find the range of .

Explain why  has an inverse.

Find .

State the domain of .

Given that , find the exact solution of .

Solve .

The functions  and  are defined as follows.

Find the range of .

Write down the range of .

Find the exact solution of the equation , giving your answer as a single logarithm

Given that the minimum value of  occurs when , explain why  has an inverse.

On the axes below, sketch the graph of  and the graph of .
Label each graph and state the intercepts on the coordinate axes.

for   for

(i) Write down the range of  and the range of .

(ii) Find.

(iii) Hence find  .

(iv) On the axes below, sketch the graphs of  and  . State the intercepts with the coordinate axes and the equations of any asymptotes.

The function is defined by.

Sketch the graph of  and hence sketch the graph of  on the axes below.

The function  is defined by .

(i) Find an expression for  and state its domain and range.

[4]

(ii) Find and simplify an expression for .

[2]

(iii) Explain why the function  does not exist.

[1]

Find the range of  and of .

Find the exact solution of  .

Find the solution of .