Question

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

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