What is the domain and range of $f (x) = \sqrt{x^{2} - 36}$ $f(x) = sqrt(x^2-36)$ ?

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Answer 1 · 2018-04-03T12:40:15

Domain: $x \leq - 6$ $x <= -6$ and $x \geq 6$ $x >= 6$
Range: all real y

graph{sqrt(x^2-36) [-10, 10, -5, 5]}

From the graph,
Domain: $x \leq - 6$ $x <= -6$ and $x \geq 6$ $x >= 6$
Range: all real y

You can also think about the domain as the part where the x-value has a corresponding y-value

Say you sub x=5, you will not get a solution because you cannot squareroot a negative number so you know that your domain should not include a x=5

What is the domain and range of f(x)=√x2−36f(x) = sqrt(x^2-36)?