To find: the function g : R → R : g o f = f o g = I_g

Formula used: (i) g o f = g(f(x))

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

Given: f : R → R : f(x) = 10x + 7

We have,

f(x) = 10x + 7

Let f(x) = y

⇒ y = 10x + 7

⇒ y – 7 = 10x

Let where g: R → R

g o f = g(f(x)) = g(10x + 7)

= x

= I_g

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

=

= x – 7 + 7

= x

Clearly g o f = f o g = I_g