Find the domain and the range of the re...

Find the domain and the range of the real function f defined by `f(x)=sqrt((x-1))`.

Text Solution

AI Generated Solution

To find the domain and range of the function \( f(x) = \sqrt{x - 1} \), we will follow these steps: ### Step 1: Determine the Domain The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function \( f(x) = \sqrt{x - 1} \), the expression under the square root must be non-negative, since the square root of a negative number is not defined in the set of real numbers. We set up the inequality: \[ x - 1 \geq 0 ...

Topper's Solved these Questions

RELATIONS AND FUNCTIONS
NCERT ENGLISH|Exercise EXERCISE 2.3|5 Videos
RELATIONS AND FUNCTIONS
NCERT ENGLISH|Exercise EXERCISE 2.1|10 Videos
PROBABILITY
NCERT ENGLISH|Exercise All Questions|71 Videos
SEQUENCES AND SERIES
NCERT ENGLISH|Exercise EXERCISE 9.5|6 Videos

The domain and range of the real function f defined by (x)/(|x|) are

Domain = R, Range = {-1, 1}

Domain = R - {0}, Range = (-1,0,1}

Domain = R - {0}, Range = {-1, 1}

Domain = R, Range = {-1,0, 1}

The domain and range of the real function f defined by f(x)=(1)/(4x^(2)-1) are

Domain `={-(1)/(2),(1)/(2)}`, Range `=-{-oo,-1)uu(0,oo)`

Domain `R={-(1)/(2),(1)/(2)}`, Range `=-{-oo,-1)uu(0,oo)`

Domain `=[-(1)/(2),(1)/(2)]`, Range `=-{-oo,-1)uu(0,oo)`

Domain `=R-[-(1)/(2),(1)/(2)]`, Range `=-{-oo,-1)uu(2,oo)`

The domain and range of the real function f defined by f(x)=(x-2)/(2-x) are

Domain = R - {2}, Range = {-1}

Domain = R-{-2), Range = {-1}

Domain = R{2}, Range = {1}

Domain =R- {2}, Range = {1}