Question

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

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

Answer 1

The correct option is B $\pm 2$

Let $f\left[g\right(x\left)\right]=25$. Since $g\left(x\right)=x^2+7$,
$f\left[g\right(x\left)\right]=25\Rightarrow f(x^2+7)=25$.
Also since $f\left(x\right)=2x+3$,
$f(x^2+7)=25\Rightarrow 2(x^2+7)+3=25$
$\Rightarrow 2x^2+17=25$
$\Rightarrow x^2=4$
$\Rightarrow x=\pm 2$.