Question Bank | Unit 13

1. Given that $f (x) = 3 x^{2} + x$ , find

(a) $f (2)$ ,

(b) $f (- 1)$ ,

(c) $f (a + 1)$ .

2. If $h (x) = 5 - 2 x^{2}$ , find $k$ such that $h (k) = - 3$ .

3. A function $f (x)$ is defined by $f (x) = \frac{2}{x + 1}$ .

(a) Evaluate $f (0)$ .

(b) Find an expression for $f^{- 1} (x)$ in terms of $x$ .

4. Given $g (x) = x^{2} - x$ . Find

(a) $g (4)$ ,

(b) $g^{- 1} (6)$ .

5. A function $k (x)$ is defined by $k (x) = \frac{x + 1}{x + 2}$ , $x \neq - 2$ .

Find the function $k^{- 1} (x)$ .

6. Given that $f : x \mapsto 17 - 4 x$ , find

(a) the value of $f (3)$ ,

(b) an expression for $f^{- 1}$ .

7. Given that $f (x) = 4 x + 3$ , evaluate

(a) $f (- 2)$ ,

(b) $f^{- 1} (31)$ .

8. Given that $f (x) = 3 x - 5$ , evaluate

(a) $f (- 4)$ ,

(b) $f^{- 1} (7)$ .

9. Given that $f : x \mapsto \frac{2 x - 7}{3}$ , find

(a) $f (2)$ ,

(b) an expression for $f^{- 1}$ .

10. Given that $f (x) = 5 - 2 x$ , find

(a) $f (- 2)$ ,

(b) $f^{- 1} (x)$ .

11. It is given that $f (x) = 2 x - 7$ and $g (x) = x (x - 6)$ .

(a) Find the value of $f (- 5)$ .

(b) (i) Obtain an expression for $f^{- 1} (x)$ .

(ii) Find the value of $f^{- 1} (15)$ .

(c) Find the values of $x$ for which

(i) $g (x) = 0$ ,

(ii) $f (x) = g (x)$ .

12. Given that $f (x) = \frac{2 x + 3}{5}$ , find

(a) $f (6)$ ,

(b) $f^{- 1} (7)$ .

13. Given that $f (x) = \frac{2 x - 1}{5}$ , find

(a) $f (8)$ ,

(b) $f^{- 1} (7)$ .

14. Given that $f : x \mapsto \frac{3 x - 5}{2}$ , find

(a) $f (3 \frac{1}{3})$ ,

(b) an expression for $f^{- 1}$ .

15. Given that $f (x) = \frac{x + 3}{2}$ , find $f^{- 1} (x)$ .

16. Given that $f (x) = \frac{x - 2}{3}$ , find $f^{- 1} (x)$ .

17. Given that $f : x \mapsto \frac{7 - 3 x}{4}$ , find

(a) $f (- 3)$ ,

(b) an expression for $f^{- 1}$ .

18. Given that $f (x) = \frac{3 x + 2}{x}$ ,

(a) find $f (- 4)$ ,

(b) find $x$ when $f (x) = 4$ ,

(c) write down the value of $f^{- 1} (4)$ .

19. It is given that $f (x) = \frac{5 - 2 x}{3}$ . Find

(a) $f (\frac{1}{2})$ ,

(b) $f^{- 1} (- 12)$ .

20. Given that $f : x \mapsto 2 x + 1$ , find an expression for $f^{- 1}$ .

21. Given that $f (x) = \frac{1}{4} (3 x + 1)$ , find

(a) $f (5)$ ,

(b) $f^{- 1} (7)$ .

22. Given that $f : x \mapsto \frac{2 x - 3}{5}$ , find

(a) $f (4)$ ,

(b) an expression for $f^{- 1}$ .

23. Given that $f : x \mapsto \frac{x + 6}{2x}$ , find

(a) $f (4)$ ,

(b) an expression for $f^{- 1} (x)$ .

Unit 13

Functions