Question

8) y= V1-5 A) Domain: x 20 Range: y 2-5 B) Domain: x > 0 Range: y'z 5 C) Domain: {All real numbers. } Range: {All real numbers. } D) Domain: x 25 Range: y 20

Answer 1

`y=\sqrt[]{x}-5`

Domain:

we know that a root cannot have negative values ​​inside so

`\begin{gathered} \sqrt[]{x}\ge0 \\ x\ge0^2^{} \\ x\ge0 \end{gathered}`

the domain is X >= 0

Range:

we solve the equation for y

`\begin{gathered} y=\sqrt[]{x}-5 \\ y+5=\sqrt[]{x} \\ (y+5)^2=x \end{gathered}`

and we replace the condition that x must be greater than or equal to 0

so

`(y+5)^2\ge0`

now solve y

`\begin{gathered} y+5\ge0^2 \\ y+5\ge0 \\ y\ge-5 \end{gathered}`

so the range is Y >= -5

then the right option is A