Q. 13.8( 34 Votes )

# Let f: R →<

It is given that f: R R be defined as f (x) = 10x + 7

Let f(x) = f(y), where x, y ϵ R.

10x + 7 = 10y + 7

x = y

f is a one – one function.

For y ϵ R, let y = 10x + 7.

x = Therefore, for any y ϵ R, there exists x = such that f is onto.

f is an invertible function.

Let us define g : R R as Now, we get:

gof(x) = g(f(x)) = g(10x + 7) And, gof = IR and gof = IR

Therefore, the required function g : R R is defined as .

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