Use function composition to show that f(x) and g(x) are inverses of each other.

Question

f(x)= 1/2x + 1 g(x)=2x-2?

Answer 1

The functions f(x) = (1/2)x+ 1 and g(x) = 2x - 2

If the two functions f(x) and g(x) are inverse to each other then (fog)(x) = (gof)(x) = x.

(fog)(x) = f(g(x))

Substitute the expression for functioning g  (in this case 2x - 2) for g(x) in the composition.

= f(2x - 2)

Now substitute this expression (2x - 2) in to function f  in place of the x value.

= [(1/2)(2x - 2)] + 1

=x - 1 + 1

= x

(gof)(x) = g(f(x))

Substitute the expression for functioning f  (in this case (1/2)x + 1) for f(x) in the composition.

= g[(1/2)x+ 1]

Now substitute this expression (1/2)x+ 1 in to function g  in place of the x value.

= 2[(1/2)x + 1] - 2

=x + 2 - 2

= x

(fog)(x) =x and  (gof)(x) = x.

f(x) and g(x) are inverse functions.