Question

If $f\left(x\right)=|x|$ and $g\left(x\right)=|x|$, then evaluate: $\left(fog\right)\left(\frac{5}{2}\right)-\left(gof\right)(-\frac{5}{2})$

• A. $2$
• B. $-4$
• C. $4$
• D. $0$

Answer 1

The correct option is D $0$

If $f\left(x\right)=|x|$ & $g\left(x\right)=|x|$

$fog\left(\frac{5}{2}\right)-gof\left(\frac{-5}{2}\right)$

$g\left(\frac{5}{2}\right)=\frac{5}{2},f\left(g\right(x\left)\right)=|g\left(x\right)|$

$f(-\frac{5}{2})=\frac{5}{2}$

$\because g\left(\frac{5}{2}\right)=\frac{5}{2}$

$g\left(f\right(x0)=|f(x)|$

$g\left(f(-\frac{5}{2})\right)=\left|f(-\frac{5}{2})\right|=\frac{5}{2}$

$\because fof\left(\frac{5}{2}\right)-gof(-\frac{5}{2})$