This math topic focuses on determining the domain of functions in which the variable is in the denominator under a square root in expressions like \(f(x) = \frac{a}{\sqrt{bx+c}}\). The skill practiced involves analyzing these functions to identify the range of x-values that will make the function’s denominator (and thus the function as a whole) valid, i.e., ensuring the expression under the square root is non-negative. This is essential for handling functions with potential restrictions on the domain due to square roots and divisions by zero. The problems typically present a math expression alongside multiple possible number line representations of its domain for selection.

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Function Domain - Fraction Integer over Root of Linear to Number Line

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What number line shows the domain of this function?

f(x)=31x+1f(x) = \frac{3}{\sqrt{1x+1}}

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