Home
Class 12
MATHS
Find the domain of the function : f(x)=1...

Find the domain of the function : `f(x)=1/(sqrt((log)_(1/2)(x^2-7x+13)))`

Text Solution

Verified by Experts

The correct Answer is:
`(3,4)`
`f(x)=(1)/(sqrt(log_(1//2)(x^(2)-7x+13)))` exists if
`log_(1//2)(x^(2)-7x+13) gt 0`
or `x^(2)-7x+13 lt 1 " (1) " `
and `x^(2)-7x+13 gt 0 " (2)" `
or `x^(2)-7x+12 lt 0 " and " (x-(7)/(2))^(2)+(3)/(4) gt 0`
or `3 lt x lt 4 " and " x in R`
or ` 3 lt x lt 4`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.9|13 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.10|6 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.7|5 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the domain of the function : f(x)=sin^(-1)((log)_2x)

Find the domain of the function : f(x)=sin^(-1)((log)_2x)

Find the domain of the function f(x)=sin^(-1)sqrt(x-1)

Find the domain of the function f(x)=sin^(-1)sqrt(x-1)

Find the domain of the function f(x) = sin^-1 sqrt(x-1)

Let x in (0,pi/2)dot Then find the domain of the function f(x)=1/sqrt((-(log)_(sinx)tanx))

Find the domain of the function : f(x)=sqrt(((log)_(0. 3)|x-2|)/(|x|))

The domain of the function f(x)=sqrt(log((1)/(|sinx|)))

Find the domain of the function : f(x)=sqrt((log)_(10){((log)_(10)x)/(2(3-(log)_(10)x)}}

Find the domain of function f(x)=3/(sqrt(4-x^(2)))log(x^(3)-x)