If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?

Asked by Aaryan | 1 year ago |  24

##### Solution :-

Given f(x) = sin x and g(x) = 2x

We know that

f: R→ [−1, 1] and g: R→ R

Clearly, the range of f is a subset of the domain of g.

gof: R→ R

(gof) (x) = g (f (x))

= g (sin x)

= 2 sin x

Clearly, the range of g is a subset of the domain of f.

fog: R → R

So, (fog) (x) = f (g (x))

= f (2x)

= sin (2x)

Clearly, fog ≠ gof

Hence they are not equal functions.

Answered by Sakshi | 1 year ago

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