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 . &nbsp0 B . &nbsp1 C . &nbsp-1 D . &nbspπ

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 th

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))))

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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