Question

Find $g\left(x\right)$, if $f\left(x\right)=5x^2+4$ and $f\left(g\right(3\left)\right)=84$

• A. $3x-10$
• B. $4x-7$
• C. $6x-17$
• D. $x^2-5$
• E. $x^2-3$

Answer 1

The correct option is D $x^2-5$

Given, $f\left(x\right)=5x^2+4$, $f\left(g\right(3\left)\right)=84$

$\Rightarrow f\left(g\right(3\left)\right)=5{g\left(3\right)}^2+4=84$

$\Rightarrow 5{g\left(3\right)}^2=80$
$\Rightarrow g\left(3\right)=\sqrt{16}=4$
$\Rightarrow g\left(x\right)=x^2-5$ satisfies the relation $g\left(3\right)=4$
Therefore, the correct option is $D$.