If f(x) = 1/x, and g(x) = sqrt(x-2), how do you find the domain and range of (f o g)(x)?

D:$\left(2 , + \infty\right)$
R:$\left(0 , + \infty\right)$

Explanation:

Given : $f \left(x\right) = \frac{1}{x}$ and $g \left(x\right) = \sqrt{x - 2}$

$f \left(g \left(x\right)\right) = \frac{1}{g} \left(x\right) = \frac{1}{\sqrt{x - 2}}$

Range should be $x > 2$ or $\left(2 , \infty\right)$. It cannot include 2 because that will make the function undefine because of $\frac{1}{\sqrt{0 - 0}}$

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