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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