8.6. Functions

Question 1

f(x) = (2x+5)²

f(x) = 2

Answer 1

(2*2 + 5)²

= 9²

= 81

Question 2

f(x) = 3x + 2

g(x) = x²

fg(x)

Eg. fg(2)

Answer 2

Begin by doing g(x), then apply f(x) onto the result of g(x).

g(2) = 2² = 4

f(4) = 3x + 2

fg(x) = 14

Question 3

How an inverse function works

Answer 3

If a function maps a number ‘n’ onto ‘m’, then the inverse function f⁻¹ maps ‘m’ onto ‘n’

Question 4

Find the inverse function of…

f(x) = 5x - 23

Answer 4

Let y = 5x - 23

Rearrange this equation to find x

3y = 5x - 2
3y + 2 = 5x
3y + 25 = x

To find the inverse function, interchange x and y

f⁻¹(x) = 3x + 25