Evaluate Using the Given Value f(r^2)=(r^2)/(|r^2|)

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

Step 1

Divide each term in $f r^{2} = \frac{r^{2}}{| r^{2} |}$ by $r^{2}$ .

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

Step 2

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

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

Divide $f$ by $1$ .

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

Step 3

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{r^{2}}{| r^{2} |} \cdot \frac{1}{r^{2}}$

Combine.

$f = \frac{r^{2} \cdot 1}{| r^{2} | r^{2}}$

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$f = \frac{r^{2} \cdot 1}{| r^{2} | r^{2}}$

Rewrite the expression.

$f = \frac{1}{| r^{2} |}$

Remove non-negative terms from the absolute value.

$f = \frac{1}{r^{2}}$