Question

What is the range of the function f(x) = |x – 5| – 3? R: {f(x) ∈ ℝ | f(x) > 2} R: {f(x) ∈ ℝ | f(x) < 2} R: {f(x) ∈ ℝ | f(x) ≥ –3} R: {f(x) ∈ ℝ | f(x) ≤ –3}

Answer 1

Given,

The expression is,

$f(x)=|x-5|-3$

Required

The range of the function.

The range of the function is calculated by taking,

$\begin{gathered} f(5)=|5-5|-3=-3 \\ f(4)=\lvert4-5\rvert-3=-2 \\ f(6)=\lvert6-5\rvert-3=-2 \\ f(3)=\lvert3-5\rvert-3=-1 \\ f(7)=\lvert7-5\rvert-3=-1 \end{gathered}$

From the above data , it is clear that the set of the output values have the values greater than or equal to -3.

Hence, range of the function is R: {f(x) ∈ ℝ | f(x) ≥ –3}.