Martin asked in Science & MathematicsMathematics · 2 months ago

Finding the domain of a function?

Say you were finding the domain of a function with a square root in the denominator. You would set it >=0 correct? but since you look at the denominator to find the domain of a function cant we just make it >0? im confused as to why we use >=0

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• TomV
Lv 7
2 months ago

If the square root is in the denominator of a rational function, the value of the expression under the radical must be greater than zero for the function to be defined and real valued. In that case, you would not use ≥ 0 because if it were 0, the function would be undefined because of division by zero.

If the square root is not in the denominator, than you can use ≥ 0 because a zero value for the square root would not be a division by zero.

So, it depends on whether the square root is in the numerator, in which case the radicand must be ≥ 0, or in the denominator in which case the radicand cannot be zero but must be > 0.