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 $x$ such that $g\left(f\right(x\left)\right)=8$?

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

Answer 1

Answer: (C)

$-1,-2$

Given, $f\left(x\right)=2x+3$

Also given $g\left(x\right)=x^2+7$

Therefore, $g\left[f\right(x\left)\right]={\left(f\right(x\left)\right)}^2+7$

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

Thus ${(2x+3)}^2+7=8\Rightarrow {(2x+3)}^2=1\Rightarrow 2x+3=\pm 1\Rightarrow 2x=\pm 1-3\Rightarrow 2x=-2,-4\Rightarrow x=-1,-2$

Option C is correct.