What is the range of the function f(x) = |x| + 5? R: f(x) < 5 R: f(x) ∈ ℝ R: f(x) ∈ ℝ R: f(x) ∈ ℝ

Question

What is the range of the function f(x) = |x| + 5? R: f(x) < 5 R: f(x) ∈ ℝ R: f(x) > 5 R: f(x) ≤ 5

Answer 1

Given:

`f(x)=|x|+5`

Find-: Range of a function.

Sol:

For |x| is always positive because |x| function is:

`|x|=\begin{cases}-x\text{ at x<0} \\ x\text{ at x>0}\end{cases}`

So the range is:

`\lbrace f(x)\in\Re|f(x)\ge5\rbrace`