Question

If $f(x,y)=(\max (x,y){)}^{\min (x,y)}$ and $g(x,y)=\max (x,y)-\min (x,y)$, then$f\left(g\left(-1,-\frac{3}{2}\right),g(-4,-1.75)\right)$ equals

• A. - 0.5
• B. 0.5
• C. 1
• D. 1.5

Answer 1

Answer: (D)

$g\left(-1,-\frac{3}{2}\right)=\max \left(-1,-\frac{3}{2}\right)-\min \left(-1,-\frac{3}{2}\right)=-1-\left(-\frac{3}{2}\right)=\frac{1}{2}$
and$g(-4,-1.75)=\max (-4,-1.75)-\min (-4,-1.75)=-1.75-(-4)=2.25=\frac{9}{4}$
Then
$f\left(\frac{1}{2},\frac{9}{4}\right)={\left(\max \left(\frac{1}{2},\frac{9}{4}\right)\right)}^{\min \left(\frac{1}{2},\frac{9}{4}\right)}={\left(\frac{9}{4}\right)}^{\frac{1}{2}}=\frac{3}{2}]$