If f: R → R ,g : R → R and h: R → R are such that f ( x ) = x 2 , g ( x ) = t a n x and h ( x ) = l o g x , then the value of ( h ( g ( f ( x ) ) ) ) if x = √ π 4 will be Options: A . &nbsp 0 B . &nbsp 1 C . &nbsp -1 D . &nbsp π

Answer: Option A : A ( h o ( g o f ) ) ( x ) = h { g { f ( x ) } } = h { t a n x 2 } = l o g { t a n x 2 } ∴ A t x = √ π 4 ⇒ ( h o ( g o f ) ) ( x ) = l o g t a n π 4 = log 1 = 0

If f: R → R ,g : R → R and h: R → R are such

Discussion Forum : Relations And Functions Ii

Question -

If f: R $\to$ R ,g : R $\to$ R and h: R $\to$ R are such that $f (x) = x^{2}$ , $g (x) = t a n x$ and $h (x) = l o g x$ , then the value of $(h (g (f (x))))$
if $x = \sqrt{\frac{π}{4}}$ will be

Options:

A . 0

B . 1

C . -1

D .

π

Answer: Option A
:
A

(h o (g o f)) (x) = h {g {f (x)}}

= h {t a n x^{2}} = l o g {t a n x^{2}}

∴ A t x = \sqrt{\frac{π}{4}} \Rightarrow (h o (g o f)) (x) = l o g t a n \frac{π}{4}

= log 1 = 0

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Discussion Forum : Relations And Functions Ii

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