If f, g, h are real functions given by f(x) = x², g(x) = tan x and h(x) = log_e x, then write the value of (hogof) $(\sqrt{\frac{π}{4}})$ .

Open in App

Solution

Given : f(x) = x², g(x) = tan x and h(x) = log_e x.
(hogof) $(\sqrt{\frac{π}{4}})$ = $h (g (f (\sqrt{\frac{π}{4}})))$
$= h (g ({(\sqrt{\frac{π}{4}})}^{2})) = h (g (\frac{π}{4})) = h (\tan (\frac{π}{4})) = h (1) = \log_{e} 1 = 0$

Suggest Corrections

Similar questions

If f, g, h are real functions given by $f (x) = x^{2}, g (x) = t a n x$ and $h (x) = l o g_{e} x$ , then write the value of $h o g o f (\sqrt{\frac{π}{4}})$

Q. If f : R

\to

R, g : R

\to

R and h : R

\to

R is such that

f (x) = x^{2}, g (x) = t a n x

and

h (x) = l o g x

, then the value of [ho(gof)], if

x = \frac{π}{2}

will be

Q. Let f, g and h be function defined as follows

f (x) = x + 2, g (x) = 3 x - 1, h (x) = 2 x

, Then

h o (g o f)

Q. Assertion :Let

f (x) = tan x

and

g (x) = x^{2}

then

f (x) + g (x)

is neither even nor odd function. Reason: If

h (x) = f (x) + g (x)

, then

h (x)

does not satisfy the condition

h (- x) = h (x)

and

h (- x) = - h (x)

If f, g, h are real functions defined by $f (x) = \sqrt{x + 1}, g (x) = \frac{1}{x}$ and $h (x) = 2 x^{2} - 3$ , then find the values of (2f + g - h) (1) and (2f + g - h) (0).

Join BYJU'S Learning Program

If f, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge x, then write the value of (hogof) π4.

Given : f(x) = x2, g(x) = tan x and h(x) = loge x. (hogof) π4 = hgfπ4 = hgπ4 2= hgπ4= htan π4= h1= loge 1 =0

If f, g, h are real functions given by f(x) = x², g(x) = tan x and h(x) = log_e x, then write the value of (hogof) $(\sqrt{\frac{π}{4}})$ .

Given : f(x) = x², g(x) = tan x and h(x) = log_e x.
(hogof) $(\sqrt{\frac{π}{4}})$ = $h (g (f (\sqrt{\frac{π}{4}})))$
$= h (g ({(\sqrt{\frac{π}{4}})}^{2})) = h (g (\frac{π}{4})) = h (\tan (\frac{π}{4})) = h (1) = \log_{e} 1 = 0$