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Question
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)=+sqrtx` , find fog and gof. Are they equal functions ?
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Solution
Given, f : R+ → R+ and g : R+ → R+
So, fog : R+ → R+ and gof : R+ → R+
Domains of fog and gof are the same.
(fog) (x) = f `(g (x)) = f (sqrtx) = (sqrtx)^2 = x`
(gof) (x) = `g (f (x)) = g (x)^2 = sqrt x^2 = x`
So, (fog) (x) = (gof) (x), ∀x ∈ R+
Hence, fog = gof
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