Question

evaluate the function ( f(x) = \frac{x}{|x|} ) at the given values of the independent variable and simplify.
a. ( f(7) )
b. ( f(-7) )
c. ( fleft( \frac{7}{2}
ight)
a. ( f(7) = square ) (simplify your answer.)
b. ( f(-7) = square ) (simplify your answer.)
c. ( fleft( \frac{7}{2}
ight) = square ) (simplify your answer.)

Explanation:

Step1: Substitute x=7 into f(x)

$f(7)=\frac{7}{|7|}$

Step2: Simplify absolute value and fraction

$|7|=7$, so $\frac{7}{7}=1$

Step3: Substitute x=-7 into f(x)

$f(-7)=\frac{-7}{|-7|}$

Step4: Simplify absolute value and fraction

$|-7|=7$, so $\frac{-7}{7}=-1$

Step5: Substitute x=r² into f(x)

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

Step6: Simplify absolute value and fraction

For any real r, $r^2\geq0$, so $|r^2|=r^2$, thus $\frac{r^2}{r^2}=1$

Answer:

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