Question

If $f\left(x\right)=a(x^n+3);f\left(1\right)=12,f\left(3\right)=36;$ then $f\left(2\right)$ is equal to

• A. $18$
• B. $24$
• C. $21$
• D. $27$

Answer 1

The correct option is A $18$

$f\left(x\right)=a(x^n+3)$

$f\left(1\right)=12$

$f\left(3\right)=36$

$f\left(1\right)=12$

$a\left(\right(1{)}^n+3)=12$

$a\left(4\right)=12$

$a=3$

$f\left(3\right)=a(3{)}^n+3)$

$36=3(3^n+3)$

$3^n+3^n+3=12$

$3^n=9$

$3^n=3^2$

$n=2$

$\begin{array}{cc}\text{Hence}f\left(x\right)& =3(x^2+3)\\ \text{now,}f\left(2\right)& =3((2^2+3)\\ & =3(4+3)\\ & =3\times 7\\ & =21\end{array}$

Correct option is$C.$