Question

If $f:R\to R$ and $g:R\to R$ are defined by $f\left(x\right)=2x+3,g\left(x\right)=x^2+7$, what are the values of $x$ for which $f\left[g\right(x\left)\right]=25$?

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

The correct option is B $\pm 2$

Given, $f\left(x\right)=2x+3$ and $g\left(x\right)=x^2+7$

$f\left[g\right(x\left)\right]=2g\left(x\right)+3\Rightarrow f\left[g\right(x\left)\right]=2(x^2+7)+3\Rightarrow f\left[g\right(x\left)\right]=2x^2+17$

Thus $2x^2+17=25$

$\Rightarrow 2x^2=8\Rightarrow x^2=4\Rightarrow x=\pm 2$

Option $B$ is correct.