Q. 64.5( 2 Votes )

Let R+ be the set of all non – negative real numbers. If f: R+ R+ and g: R+ R+ are defined as f(x) = x2 and g(x) = + √x. Find fog and gof. Are they equal functions.

Answer :

We have, f : R+ R+ given by


f (x) = x2


g: R + R + given by



fog (x) = f(g(x)) = f(= ()2 = x


Also,


gof (x) = g(f(x)) = g(x2) = = x


Thus,


fog(x)= gof (x)


They are equal functions as their domain and range are also equal.


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