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# 1. Let f(x) = 7 – 2x and g(x) = x + 3. (a) Find (g ° f)(x).

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IB Questionbank Maths SL 1

1. Let f(x) = 7 – 2x and g(x) = x + 3.

(a) Find (g ° f)(x).

(2)

(b) Write down g–1(x).

(1)

(c) Find (f ° g–1)(5).

(2) (Total 5 marks)

2. Let f(x) = 3x, g(x) = 2x – 5 and h(x) = (f ° g)(x).

(a) Find h(x).

(2)

(b) Find h–1(x).

(3) (Total 5 marks)

3. Let f(x) = x2 and g(x) = 2x – 3.

(a) Find g–1(x).

(2)

(b) Find (f ° g)(4).

(3) (Total 5 marks)

(2)

IB Questionbank Maths SL 2

4. The functions f and g are defined by f : x  3x, g : x  x + 2.

(a) Find an expression for (f ° g)(x).

(2) (b) Find f–1(18) + g–1(18).

(4) (Total 6 marks)

5. Let f (x) = 2x + 1 and g (x) = 3x2 – 4.

Find

(a) f –1(x);

(b) (g  f ) (–2);

(c) ( f  g) (x).

Working:

(a) ………..

(b) ………..

(c) ………..

(Total 6 marks)

(3)

IB Questionbank Maths SL 3

6. Consider the functions f : x 4(x – 1) and g : x  2 –

6 x

.

(a) Find g–1.

(b) Solve the equation ( f ° g–1) (x) = 4.

Working:

(a) ...

(b) ...

(Total 6 marks)

(4)

IB Questionbank Maths SL 4

7. Two functions f, g are defined as follows:

f : x  3x + 5 g : x  2(1 – x)

Find

(a) f –1(2);

(b) (g f )(–4).

Working:

(a) ...

(b) ...

(Total 4 marks)

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