The composite mapping fog of the maps `f:R to R , f(x)=sin x and g:R to R, g(x)=x^(2)`, is

Options

A. `x^(2)` sin x
B. `(sin x)^(2)`
C. `sin x^(2)`
D. `sin x//x^(2)`

Answer

C

Explanation

`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)`