Q19 of 99 Page 53

Let f : R → R : f(x) = 10x + 7. Find the function g : R → R : g o f = f o g = Ig.

To find: the function g : R → R : g o f = f o g = Ig


Formula used: (i) g o f = g(f(x))


(ii) f o g = f(g(x))


Given: f : R → R : f(x) = 10x + 7


We have,


f(x) = 10x + 7


Let f(x) = y


⇒ y = 10x + 7


⇒ y – 7 = 10x



Let where g: R → R


g o f = g(f(x)) = g(10x + 7)


= x


= Ig


f o g = f(g(x)) =


=


= x – 7 + 7


= x


Clearly g o f = f o g = Ig


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