1. Given the function f(x) = 6x + 1. Find the value of p if f(4) = 4p + 5.

2. Function f is defined as f(x) = 5

2 x−1, x ≠ k. Find the value of k.

3. Given g(x) = 3 x−52x+7 . Function g is defined for all values of x except x = a. Find the value of

a.

4. Given the function f(x) = 3x + 2, find the value ofa. f(2)b. f(-5)

c. f ( 13)

5. If f(x) = x2 + 3x + 2, express each of the following in terms of x:a. f(2x)b. f(3x + 1)c. f(x2)

6. If f(x) = x + 5 and g(x) = x2 + 2x + 3, finda. gf(2)b. fg(2)c. fg(x)d. gf(x)e. g2(x)f. f2(x)

7. Function f and g are defined by f(x) = x – 1 and g(x) = 3−xx+4 . Find

a. gf(3)b. fg(-1)c. fg(x)d. gf(x)e. g2(x)f. f2(x)

8. If f(x) = 2x + 1 and g(x) = 5x

, x ≠ 0. Find the composite function gf(x), fg(x), and the value of

gf(4).

9. Given f(x) = 1 – x and g(x) = px2 + q. If the composite function gf is defined by gf(x) = 3x2 – 6x +5, find the value of p, q and g2(-1).

10. Given f(x) = hx + k and f2(x) = 4x + 15. a. Find the values of h and k

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b. Take h > 0, find the values of x for which f(x2) = 7x

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11. A function f is defined by f(x) = 2x . Find the function g if fg(x) = x2 + 1.

12. A function f is defined by f(x) = 2x + 1. Find the function g if fg(x) = 5 x−2x+5

, x≠ 5.

13. A function f is defined by f(x) = x – 1. Find the function g if gf(x) = 4

x+2, x ≠−2.

14. A function f is defined by f(x) = 7x . Find the function g if gf(x) =

102 x+3

, x ≠− 32 .

15. Find the inverse function of the following function:a. f(x) = 4 – 7x

b. f(x) = 2 x+5

3

c. f(x) =5

7 x

d. f(x) = 2

3−x

e. f(x) = 3 x+25 x+3

16. If f(x) = x – 2, find f -1(5).

17. If f(x) = x+9x−5

, x ≠ 5, find f -1(3).

18. If g(x) = m−xx−3

, x≠ 3 and g -1(5) = 14. Find the value of m.

19. If f(x) = mx−nx−2

, x≠ 2 and f -1(x) = 5−2 x2−x

, x≠ 2. Find the value of m and n.

20. Given that f(x) = 2 h

x−3 k, x≠ 3 k , where h and k are constants and f -1(x) =

14+24 xx

, x≠ 0, find

the value of h and k.

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