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)=$$+ \sqrt{x}$$, find fog and gof. Are they equal functions.

Asked by Sakshi | 1 year ago |  116

##### 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.

Now we have to find fog and gof also we have to check whether they are equal or not,

Consider (fog) (x) = f (g (x))

= $$f (\sqrt{x})$$

$$\sqrt{x^2}$$

= x

Now consider (gof) (x) = g (f (x))

= g (x2)

$$\sqrt{x^2}$$

= x

So, (fog) (x) = (gof) (x), ∀x ∈ R+

Hence, fog = gof

Answered by Aaryan | 1 year ago

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