The range of the functionf x -cos 2 x -4-sin x -4- x - R is-1- 5-4-B- -1- 5-4-C- -1- 5-4D -0- 5-4-

The correct option is B f(x)=1 sin^2 x/4+sinx/4= { sin^2x/4 sinx/4}+1 = { ( sin x/4 1/2 )^2 1/4}+1= 5/4 ( sin x/4 1/2 )^2 Maximum f(x)=5/4 Minimum f(x)=5 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Using Monotonicity to Find the Range of a Function

The range of ...

Question

$The range of the function f (x) = c o s^{2} \frac{x}{4} + s i n \frac{x}{4}, x ϵ R i s$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D

$f (x) = 1 - s i n^{2} \frac{x}{4} + s i n \frac{x}{4} = - {s i n^{2} \frac{x}{4} - s i n \frac{x}{4}} + 1 = - {{(s i n \frac{x}{4} - \frac{1}{2})}^{2} - \frac{1}{4}} + 1 = \frac{5}{4} - {(s i n \frac{x}{4} - \frac{1}{2})}^{2} Maximum f (x) = \frac{5}{4} Minimum f (x) = \frac{5}{4} = {(- 1 - \frac{1}{2})}^{2} = \frac{5}{4} - \frac{9}{4} = - 1 Range of f (x) = [- 1, \frac{5}{4}]$

Suggest Corrections

Similar questions

Q. The range of the function

f (x) = c o s^{2} \frac{x}{4} + s i n \frac{x}{4}, x ϵ R

Q. The range of

f (x) = \frac{1}{- x^{2} + 4 x + 5}

x \in R - {- 1, 5}

Q. The values of

k

for which the equation

∣ ∣ | x - 2 | - 5 ∣ ∣ = k

has

4

distinct solutions is

Q. The range of the function

f (x) = c o s^{2} \frac{x}{4} + s i n \frac{x}{4}, x ϵ R

If A = {1, 2, 3 }, B = {4, 5, 6 }, which of the following is not a relation from A to B

Join BYJU'S Learning Program

The range of the functionf(x)=cos2x4+sinx4,xϵR is

The correct option is D f(x)=1−sin2x4+sinx4=−{sin2x4−sinx4}+1=−{(sinx4−12)2−14}+1=54−(sinx4−12)2Maximum f(x)=54Minimum f(x)=54=(−1−12)2=54−94=−1Range of f(x)=[−1,54]

$The range of the function f (x) = c o s^{2} \frac{x}{4} + s i n \frac{x}{4}, x ϵ R i s$