Q8 of 20 Page 1

Let f : R → R be defined as f(x) = 10x + 7. Find the function g : R → R such that gof = fog =IR. [CBSE 2011]

As we have to find g: R→R such that-


fog = gof = IR


We know that IR represents an identity function.


By identity function we mean that –


I(x) = x


∵ fog(x) = I(x)


⇒ f(g(x)) = x


∵ f(x) = 10x + 7


∴ fog(x) = 10{g(x)} + 7 = x


⇒ 10g(x) = x – 7


∴ g(x) =


G (x) is defined everywhere on a set of real numbers, and its range is also R.


∴ g: R→R can be defined by g(x) =


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