Question

Let $f\left(x\right)=\frac{8}{x},x\ne 0\text{and}fog\left(x\right)=4x.$ If $gof\left(x\right)=3,$ then $x$ is

• A. 12
• B. 12.00
• C. 12.0

Answer 1

Answer: (A), (B), (C)

Given, $f\left(x\right)=\frac{8}{x}\text{and}fog\left(x\right)=4x$ $\Rightarrow f\left(g\right(x\left)\right)=\frac{8}{g\left(x\right)}$
$\Rightarrow 4x=\frac{8}{g\left(x\right)}$
$\Rightarrow g\left(x\right)=\frac{2}{x}$
$\text{Thus}g\left(f\right(x\left)\right)=\frac{2}{\frac{8}{x}}=\frac{x}{4}$
$\Rightarrow 3=\frac{x}{4}$
$\Rightarrow x=12$