Let fx-x2-gx-tan x and hx-ln x-For x-2- what is the value of -hogofx-

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Definition of Functions

Let fx=x2,g...

Question

Let $f (x) = x^{2}, g (x) = tan x$ and $h (x) = l n x$ .
For $x = \frac{\sqrt{π}}{2}$ , what is the value of $[h o (g o f) (x)] ?$

0

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\frac{π}{4}

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\frac{π}{2}

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Solution

The correct option is B $0$
Given,

$f (x) = x^{2}$

$g (x) = tan x$

$h (x) = ln x$

$[h o (g o f) (x)]$

$= [h o g (x^{2})]$

$= [h o (tan x^{2})]$

$= ln tan x^{2}$

for $x = \frac{\sqrt{π}}{2}$

$[h o (g o f) (x)] = ln tan \frac{π}{4} = 0$

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Let f(x)=x2,g(x)=tanx and h(x)=lnx.For x=√π2, what is the value of [ho(gof)(x)]?

The correct option is B 0Given,f(x)=x2g(x)=tanxh(x)=lnx[ho(gof)(x)]=[hog(x2)]=[ho(tanx2)]=lntanx2for x=√π2[ho(gof)(x)]=lntanπ4=0

Let $f (x) = x^{2}, g (x) = tan x$ and $h (x) = l n x$ .
For $x = \frac{\sqrt{π}}{2}$ , what is the value of $[h o (g o f) (x)] ?$

The correct option is B $0$
Given,

$f (x) = x^{2}$

$g (x) = tan x$

$h (x) = ln x$

$[h o (g o f) (x)]$

$= [h o g (x^{2})]$

$= [h o (tan x^{2})]$

$= ln tan x^{2}$

for $x = \frac{\sqrt{π}}{2}$

$[h o (g o f) (x)] = ln tan \frac{π}{4} = 0$