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The composite mapping fog of the maps f:...

The composite mapping fog of the maps `f:RtoR,f(x)=sinx,g:RtoR,g(x)=x^(2)` is :

A

`x^(2)` sin x

B

`(sin x)^(2)`

C

`sin x^(2)`

D

`sin x//x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`f : R rarr R`
implies f(x) = sin x and `g : R rarr R`
`implies g(x) = x^(2)`
Range of g is `R^(+)uu{0}`, which is the subset of domain of f.
`therefore` Composition of fog is possible.
`fog = f(g(x)) = f(x^(2))`
`= sin x^(2)`
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