Let f ( x ) = x 2 + 4 and g ( x ) = 1 x - 1 , then

Question

Let $f (x) = x^{2} + 4$ and $g (x) = \frac{1}{\sqrt{x - 1}}$ , then

Smart Achievers · Accepted Answer

(2, 3, 4)

$dom f = ℝ and dom g = {x : x > 1} .$

Since $x^{2} \geq 0$ for any $x$ , so $range f = [4, \infty) and range g = (0, \infty) .$

Hence, $Dom (f + g) = ℝ \cap (1, \infty) = (1, \infty),$ $Range f \cap Range g = [4, \infty)$ and $Range f \cup Range g = (0, \infty) .$

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