Question

if f(x)=sinx g(x)=x^2,x element R then find (fog) (x)​

Answer 1

Hope it is helpful......

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{(fog)(x)=sin\:x^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies f(x) = sin \: x \\ \\ \tt: \implies g(x) = {x}^{2} \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies (fog)(x) =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies (fog)(x) = f(g(x)) \\ \\ \tt: \implies (fog)(x) =sin( x ) \\ \\ \tt: \implies (fog)(x) =sin( {x}^{2} ) \\ \\ \green{\tt: \implies (fog)(x) = sin\:x^{2} }\\\\ \blue{\huge{ \boxed{ \tt Some \: related \: concept}}} \\ \\ \orange{\tt \circ \: f(x) = sin \: x \to \:Period = 2\pi} \\ \\ \orange{\tt \circ \: f(x) = cos\: x \to \:Period = 2\pi} \\ \\ \orange{\tt \circ \: f(x) = tan \: x \to \:Period = \pi} \\ \\ \orange{\tt \circ \: f(x) =sec \: x \to \:Period = 2\pi} \\ \\ \orange{\tt \circ \: f(x) = cosec \: x \to \:Period = 2\pi} \\ \\ \orange{\tt \circ \: f(x) = cot \: x \to \:Period = \pi}$