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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

Verified by Experts

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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