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If f : R rarr R and g : R rarr R be two ...

If `f : R rarr R and g : R rarr R` be two mapping such that `f(x) = sin x` and `g(x) = x^(2)`, then find the values of `(fog) ((sqrt(pi))/(2))` and `(gof)((pi)/(3))`.

Text Solution

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From Eq. (i), (fog) `x = sin x^(2)`
`therefore ("fog")(sqrt(pi))/(2)=sin.(pi)/(4)=(1)/(sqrt(2))`
and from Eq. (ii), (gof) x = `sin^(2)` x
`therefore (gof)(pi)/(3)=sin^(2).(pi)/(3)=((sqrt(3))/(2))^(2)=(3)/(4)`
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