यदि `f:R to R,g: R to R` तथा `h:R to R` इस प्रकार है `f(x)=x^(2), g(x)=tan x ` `h(x)=log(x)` तो सिद्ध कीजिएः `[ho(gof)] (x)=0`, जबकि `x=(sqrtpi)/(2)`

Answer

0

Explanation

`" "[ho(gof)(x)=h(gof)(x)]`
`" "=[ho(g(f(x))]`
`" "=h[g(x^(2))]" "[therefore f(x)=x^(2)]`
`" "=h[tan x^(2)]" "[g(x)=tan x]`
`" "=log tanx^(2)" "[h(x)=log x]`
`" "=log tan((pi)/(4))" "[therefore x^(2)=(pi)/(4)]`
`" "=log 1`
`" "=0`