Consider the functions given by f x 4x and g x x 6 Find f

Consider the functions given by f x = 4x and g x = x + 6. Find f g (x) Find f g^-1 (x) Find f^-1(x) and g^-1(x) Find (g^-1 f^-1) and compare the results with that of part (b).

Solution

Solution:

Given

f(x) = 4x and g(x) = x+6

1)

( f o g )(x) = f(g(x))

= f(x+6)

= 4(x+6)

= 4x+24

2)

fog^-1(x) = (f(x).g(x))^-1

= (4x+24)^-1(x)

= x/(4x+24)

3)

f^-1(x) and g^-1(x)

f^-1(x) = (4x)^-1(x)

= 1/4

g^-1(x) = (x+6)^-1(x)

= x 1/(x+6)

= x/(x+6)

4)

(g^-1o f^-1)(x) = 1/4 * x/(x+6)

= x/(4x+24)