Question

If $f:R\to R$ and $g:R\to$ 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

$f\left(x\right)=2x+3$ and $g\left(x\right)=x^2+7$
$g\left(f\right(x\left)\right)=8\Rightarrow f(x{)}^{2}2+7=8\Rightarrow (2x+3)2+7=8\Rightarrow 4x^2+9+12x+7=8\Rightarrow 4x^2+12x+16=8\Rightarrow x^2+3x+4=2\Rightarrow x^2+3x+2=0\Rightarrow (x+2\left)\right(x+1)=0\Rightarrow x=-1,-2$