Q. 13.8( 30 Votes )

# Let f: R → R be defined as f (x) = 10x + 7. Find the function g : R → R such that g o f = f o g = 1_{R}.

Answer :

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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