FUNCTIONS

FUNCTIONS


1. The functions f,g and h are defined by
f : x--->4x-5
g : x---> 2x2
h : x--->x6+4x

a) find the value of (i) f(4) (ii)g(-3) , (iii) h(1 /2)

b) solve the equations (i) f(x) = 3, (ii) g(x) = 32, (iii) h(x) = 7

c) express the composite functions (i) gf (ii)fh in the form of gf  : x---> ……., fh : x--->
you need not simplify your answers
d) express the inverse f -1and h -1 in the form of f -1: x---> , h -1 : x--->

e) show that the equation g(x) = 5[f(x)] + 7 can be written in the form ax2 + bx + c = 0 and state the values of a,b and c.

2. f and g are defined by
f : x--->4x –1 and g : x---> 2x2 + 3

a) find the value of f(2)

b) express the inverse of the function f in the form f -1: x--->
c) express fg in the form fg : x--->
d) solve the equation fg(x) = f(x) + 24.

3. The functions f and g are defined by
f : x---> 2x2 + 1, g : x---> 7x – 5
a) find the value of x for which f(2) = g(x)
b) copy and complete the following
i) fg : x---> ii) inverse of g : x--->
c) find the values x for which f(x) = g (x)


4. Given that f : x---> x2 +3
a) find f(4), b) complete and simplify the statement ff : x--->

5. f : x ---->3x2 + 1 , g ; x 2x –1
copy , complete and simplify the following
a) gg : x---> b) gf : x---> c) g -1 : x--->

6. f : x---> 5x + 4, g : x---> 4x + 3
a) find g(2)
b) solve, for x, the equation f(x) = g(2)
c) copy and complete the following, simplifying as appropriate
i) f -1: x---> ii) ff : x--->
d) show that f (g(x)) = g (f(x))
e) solve the equation g(x) = 2 giving your answers to 2 decimal places.

7. The functions f, g and h are defined by
f : x---> 3x + 2, g : x---> x2 – 4, h : x---> x + 1
a) find the value of i) f(2) ii) g(-3) iii) h(1/4)
b) solve the equation i) f(x) = 12 ii) f(x) = h(x)
c) express the composite function gf in the form gf : x ….,simplify your answer.
8. f : x x2 – 5x≠
a) write down the value of f (-2)
b) write down the value of ff(2)
c) find the range of f when the domain is {-1, 0, 1}

9. The functions f and g are defined by
f : x---> 2x – 1 , g : x---> x2 + 8,
a) find the values of i) f(3) ii) g(-2)
b) solve the equations i) g(x) = 12 ii) g(x) = 4 f(x)
c) Express the composite functions i) fg, ii) gf in the form fg : x--->, gf : x--->
d) Show that the equation fg(x) = gf(x) can be expressed in the form x2 + bx + c = 0. Where b and c are integers, and state the values of b and c.
e) Express the inverse function, f –1, in the form, f –1 : x--->


10. The functions f,g and h are defined by f : x 2x + 1, g : x 3x2 , h : x , x ≠ 1
a) find the value of i) g (-4) ii) h(1 /2)
b) solve the equations i) g(x) = 75 ii) h(x) = 4, iii) f(x) = g(x)
c) express hf(x) in terms of x, simplifying your answer.


11. f : x---> , x ≠ -2

Given that f(x) = 3, a) find x b) find f (f(4))
Given that the domain of f is the set s = {-1,0,1}
c)find the range of s under f.

12. f : x---> x2 + 3x – 4 , g : x---> x +1
a) find i) f(-2) ii) g -1(1/2 )
b) solve the equation fg(x) = 0
c) solve the equation fg(x) = gf(x)


13. f : x---> 1 – 3x , g : x x ≠ 0

find the values of a) f(3) b) gf(1)


14. f : x---> 2x2 – 3 , g : x---> 3x + 5, copy , complete and simplify
a) gg : x---> b) fg : : x---> c) g -1 : x--->

15. f : x---> x2 – 3x – 5, g : x---> 2x + 1
a) find the value of I) f(2) ii) fg(-1 /2 )
b) express the inverse function g -1 in the form g -1 : x--->
c) express the composite function fg in the form fg : x--->
simplifying your answer
d) find the values of x for which f(x) = g(x)

16. The functions f and g are defined by
f : x---> 2x – 3, g : x , x ≠ 0

a) find the value of I) f(3), ii) gf(2)
b) find and simplify I) f -1 : x---> ii) fg : x--->
c) solve the equation fg(x) = gf(x)


FUNCTIONS ( continued)

17. The functions f and g are defined by f: x---> 3x – 2 , g : x--->2x+8 , x ≠ 2
a) find the value of I) f(2) ii) gf(10)
b) express
i) the inverse function g -1, in the form g -1 : x--->
ii) the composite function fg, in the form fg : x--->
c) solve the equation f(x) = g(x)


18. The function f is defined by f : x , x ≠3
Given that f(x) = 2
a) find the value of x
b) find the value of ff(0).

19. f : x 3x – 4 , g : x x2 + 1
copy, complete and simplify
a) fg : x ……. b) gf : x …….
c) find the two values of x for which fg(x) = gf(x)

20. Given that f : x 3x –1 ,
a) evaluate f(-1/3), b) find f -1 (x)

21. Write down the range of each of the following functions
a) f : x x2 , -3< x < 3,
b) g : x sinxo 0 < x < 90


22. f : x a 5x + 3, g : x a + 15

a ) calculate i) f (3) , ii) fg(4)
b) solve i) f(x) = 1, ii) f(x) = g(x)

23. (i) Given that f : x 6 – x2
a) state the maximum value of f(x).
b) write down the range of f.
(ii) Given that g : x , state the value of x which must be excluded from the domain of g

24. The functions f and g are defined by f : x 1 – x, g : x 2x2 + 3,
a) find the values of I) f(-2) ii) g( 2)
b) Express the inverse function f -1 in the form , f -1 : x ……
c) Express the composite function gf in the form gf : x ………simplifying your answer
d) solve the equation
i) g(x) = 53 ii) ff(x) = f(x)

25. f : x x 2 – 1, g : x 3x – 4 ,
a ) complete the following statements, simplifying your answers where appropriate
i) g-1 : x …….. ii) fg : x ……..

b) find the values of x which satisfy the equation fg(x) = 9 – 3x