Given, f(x) = 10x + 7

Now we have to find a function g : R -> R such that fog(x) = got(x) = I_R

From the definition of the inverse of a function

we can understand that this question actually require us to find the function f(x) = 10x + 7

1. Injectivity

Let x , x ∈ R

Then f(x ) = f(x)

10x + 7 = 10x + 7

=> x = x

So f(x) is a one - one function

2. Surjectivity

Let y = 10x + 7

=> y - 7 = 10x

=> x = (y - 7)/10

For every y ∈ R , we can find an x = (y - 7)/10 ∈ R such that

f(x) = f{(y – 7)/10)} 

       = 10*( y-7)/10 + 7

       = y - 7 + 7

       = y

So f(x) is a onto function.

Now define f : R -> R such that f (y) = (y – 7)/10

This function f is our required function g

So, the required function

g(x) = (x – 7)/10