Home
Class 12
MATHS
Find the range of f(x)=1/(1-3sqrt(1-sin^...

Find the range of `f(x)=1/(1-3sqrt(1-sin^2x))`

Text Solution

Verified by Experts

The correct Answer is:
`(-oo,1//2] cup [1,oo)`
`f(x)=(1)/(1-3sqrt(1-sin^(2)x))=(1)/(1-3sqrt(cos^(2)x))`
`=(1)/(1-3|cosx|)`
Now, `-3|cosx| in [-3,0]`
or `1-3|cosx| in[-2,1]`
or `(1)/(1-3|cosx|) in (-oo,-1//2] cup [1,oo)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.7|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.8|9 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x)=sqrt(4-sqrt(1+tan^2x)) .

Find the range of f(x)=sqrt(1-sqrt(x^2-6x+9))

Find the range of f(x)=1/(2cosx-1)

Find the rang of f(x)=sqrt(sin^2x-6sinx+9)+3

Find the range of f(x)=cos^(-1)((sqrt(1+2x^2))/(1+x^2))

Find the range of f(x)=1/(2abscosx-3)

Find the range of f(x) = sqrt(x-1)+sqrt(5-x)

Find the range of f(x)=tan^(-1)sqrt((x^2-2x+2))

Find the range of f(x)=sqrt(sin(cos x))+sqrt(cos(sin x)) .

Find the range of f(x)=sqrt((cos^(-1)sqrt((1-x^2))-sin^(-1)x))