Finding range for inverse function

Question

$3(\arcsin(x))^2 + 2(\arccos(x))^2+7 =f(x)$

My attempt

I wrote $\arcsin(x) = \frac{\pi}{2} - \arccos(x)$ Then I found max value of $f(x)$ Since. $0<\arccos(x) <\pi$ For f max I made $\arccos(x) = \pi$

Answer 1

HINT: Let $\arccos x=t$ and $t \in \left[ 0 \:\: \pi \right]$

Then we have $$g(t)=3\left(\frac{\pi}{2}-t\right)^2+2t^2+7$$

Maximize and Minimize $g(t)$ in $t \in \left[0 \: \:\pi \right]$