Question

If $f:R\to R$ and $g:R\to R$ are defined by $f\left(x\right)=2x+3$ and $g\left(x\right)=x^2+7$, then the values of $x$ such that $g\left(f\right(x\left)\right)=8$ are:

• A. $1,2$
• B. $-1,2$
• C. $-1,-2$
• D. $1,-2$

Answer 1

The correct option is C $-1,-2$

Since $f\left(x\right)=2x+3$,
$g\left[f\right(x\left)\right]=8\Rightarrow g(2x+3)=8$.
Also since $g\left(x\right)=x^2+7$,
$g(2+3x)=8\Rightarrow (2x+3{)}^2+7=8$
$\Rightarrow 2x+3=\pm 1$
$\Rightarrow x=-1$ or $-2$.