Question

Find the domain and range of sqrt x-2/x-1

Answer 1

Question ⤵️

Find the domain and range of sqrt x-2/x-1.

Answer ⤵️

The domain of the function will be determined by the fact that the expression that's under the radical must be positive for real numbers.

Since x² will always be positive regardless of the sign of x

, you need to find the values of x that will make x² smaller than 1.

, since those are the only values that will make the expression negative.

So, you need to have

x² − 1 ≥ 0

x² ≥ 1

Take the square root of both sides to get

| x | ≥ 1

This of course means that you have

x ≥ 1 and x ≤ −1

The domain of the function will thus be

( − ∞, −1] ∪ [ 1, + ∞ ) .

The range of the function will be determined by the fact that the square root of a real number must always be positive. The smallest value the function can take will happen for

x = −1 and for x = 1

, since those values of x

will make the radical term equal to zero.

√( − 1)² − 1 = 0 and √( 1 )² − 1 =0

The range of the function will thus be

[ 0, + ∞ ) .

graph{sqrt(x^2-1) [-10, 10, -5, 5]}

Hope it helps you ✌️

Step-by-step explanation:

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