Let R + be the set of all non – negative real numbers. If f: R + → R + and g: R + → R + are defined as f(x) = x 2 and g(x) = + √x. Find fog and gof. Are they equal functions.

Question

Philoid · Accepted 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.

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.

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.