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.

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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