Q3. - Algebra 2

Question

Write a function involving absolute value for which $f(-2)=3$

Step-by-Step Solution

Answer

The absolute value function for which $f(-2)=3 is f\left(x\right)=\left|x-1\right|$

Step-1–Absolute value

The absolute value of a number is its distance of number from zero on the number line and distance is always non-negative

Step-2 – Rewrite the given Function.

The absolute function can be written as:

$f\left(x\right)=\{\begin{array}{l}-xifx<0\\ xifx\ge 0\end{array}$

Step-3&ndash;Simplify.

Assume the equation is $f\left(x\right)=|x-1|$.

Substitute the value of x by$-2$

$\begin{array}{l}f\left(x\right)=|x-1|\\ f(-2)=|-2-1|\\ =|-3|\\ =3\end{array}$

So, the absolute value function for which $f(-2)=3 is f\left(x\right)=\left|x-1\right|$