What is the domain and range of $y = \frac{- 4}{\sqrt{x + 1}}$ $y = (-4) / ( sqrt (x +1))$ ?

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Answer 1 · 2018-06-19T15:59:26

The domain is $x \in (- 1, + \infty)$ $x in (-1, +oo)$ .
The range is $y \in (- \infty, 0^{-})$ $y in (-oo,0^-)$

The function is

$y = - \frac{4}{\sqrt{x + 1}}$ $y=-4/sqrt(x+1)$

What's under the square root sign is $\geq 0$ $>=0$ and also, the denominator $\neq 0$ $!=0$

Therefore,

$x + 1 > 0$ $x+1>0$

$\Rightarrow$ $=>$ , $x > - 1$ $x > -1$

The domain is $x \in (- 1, + \infty)$ $x in (-1, +oo)$

When $x \to - 1^{+}$ $x->-1^+$ , $\Rightarrow$ $=>$ , $y \to - \infty$ $y->-oo$

When $x \to + \infty$ $x->+oo$ , $\Rightarrow$ $=>$ , $y \to 0^{-}$ $y->0^-$

The range is $y \in (- \infty, 0^{-})$ $y in (-oo,0^-)$

graph{-4/sqrt(x+1) [-7.1, 28.93, -12.47, 5.55]}

What is the domain and range of y = (-4) / ( sqrt (x +1))y=−4√x+1 y = (-4) / ( sqrt (x +1))?