Question

evaluate the function $f(x) = \frac{x}{|x|}$ at the given values of the independent variable and simplify.
a. $f(3)$
b. $f(-3)$
c. $f(r^2)$
a. $f(3) = \square$ (simplify your answer.)
b. $f(-3) = \square$ (simplify your answer.)
c. $f(r^2) = \square$ (simplify your answer.)

Explanation:

Step1: Substitute x=3 into f(x)

$f(3)=\frac{3}{|3|}$

Step2: Simplify absolute value and fraction

$|3|=3$, so $\frac{3}{3}=1$

Step3: Substitute x=-3 into f(x)

$f(-3)=\frac{-3}{|-3|}$

Step4: Simplify absolute value and fraction

$|-3|=3$, so $\frac{-3}{3}=-1$

Step5: Substitute x=$r^2$ into f(x)

$f(r^2)=\frac{r^2}{|r^2|}$

Step6: Simplify absolute value and fraction

$|r^2|=r^2$ (since squares are non-negative), so $\frac{r^2}{r^2}=1$

Answer:

a. $1$
b. $-1$
c. $1$