Question

The function $f\left(x\right)=\frac{x^3}{4}-\sin \pi x+3$ on $[-2,2]$ takes the value

• A. $1$
• B. $\frac{7}{3}$
• C. $6$
• D. $3$

Answer 1

Answer: (A), (D)

$1$
$3$

$f\left(2\right)=\frac{8}{4}-0+3$
$=2+3$
$=5$ ...(i)
$f(-2)=-2+3$
$=1$ ...(ii)
$f\left(\frac{1}{2}\right)$
$=\frac{1}{32}-1+3$
$=\frac{65}{32}$ ...(iii)
$f(-\frac{1}{2})$
$=\frac{-1}{32}+1+3$
$=\frac{127}{32}$ ...(iv)
$f\left(1\right)=\frac{13}{4}$ and $f(-1)=\frac{11}{4}$.
And $f\left(0\right)=3$.
Thus we get
$f(-2)=1$ and $f\left(0\right)=3$.