FUNCTIONS

FUNCTIONS


The idea of functions is used in almost every branch of Mathematics.
The two common notations are
a) f(x) = x2 + 4
b) f : x2 + 4

Some more notations used in functions are as follows

Simple Functions : f(x)
Inverse Functions : f-1(x)
Composite Functions : fg(x) or f(g(x))

Grade 9
Example:-
1) Given f(x) = 3x - 1 and g(x) = 1 – x2
Find the following:-
a) i) f(2) = 5 b) i) g(2) = - 3
ii) f(0) = - 1 ii) g(-2) = -3
iii) f(-3) = -10 iii) g(1/2) = ¾
iv) f(-x) = -3x – 1 iv) g(m) = 1 – m2
v) f(k) = 3k + 1 v) g(1/t) = 1 – 1/t2

Exercise

1) Given the functions h : x x2 + 1 and g: x 10x + 1
Find the following:-

a) h(2) b) h(-1) c) h(0)
d) h(+5) e) h(1/2) f) g(k)
g) g(-m) h) g(k) i) g(1/10)
j) g(-5)



2) Given the functions f(x) = 2x – 4 , g(x) = , h(x) = (7 – 3x)2
Use the above functions to find the following

a) f -1(x)
b) f -1(8)
c) g -1(x)
d) g -1(16)
e) h-1(x)


3) Given the functions f(x) = 2x2/3 , g(x) =10 – x2 , h(x) = 2x2 + 1
Use the above functions to solve the following
a) f(x) = 5
b) f(x) = x
c) h(x) = 0
d) g(x) = 6
e) g(x) = h(x)
f) h(k) = k + 1

Grade 10

Take all the above questions also for Gr 10
These questions are also included

4) Given the functions f: x x/4 , h : x x2 + 1 and g: x 10x + 1
Find the following

a) fg(2) b) gh(3) c) f-1g(4)

d) f(x) = g(x) e) h-1f(-2) f) hg(5)


Past Paper Questions

1. (P2May/June- 2001)
Given f(x) = for x>0 and g(x) = 3 – 3x for any value of x.
a) find f( ) , giving your answer as a fraction
b) if f(x) = g(x), find the value of x
c) find f-1(x) and g-1(x)
d) g-1(18)



2.(P2, May/June 2001)


f(x) = x1/3 and g(x) = 2x2 – 5 for all values of x.
a) Find
i) g(4)
ii) f(27)
b) Find an expression for g-1(x) in terms of x.
c) Find f1(x)


3.



a) calculate i) ii)



b) find and simplify as a single fraction
of the composite function
find the inverse h-1, of the function.
c) solve for x if
Give your answer , correct to, 2 decimal places.


4. The functions f(x) and g(x) are defined as follows.

a) find the value of g (- 4)
b) find and simplify as a single fraction f(x) – g (x).
c) find an expression for f -1.
d) find an expression for g -1.