Question

Functions $f$ and $g$ are defined by $f\left(x\right)=x^2+x$ and $g\left(x\right)=\sqrt{(x+6)}$. What is the value of $g\left(f\right(2\left)\right)$?

• A. $2\sqrt{3}$
• B. $-3$
• C. $7$
• D. $6$
• E. $-6$

Answer 1

The correct option is A $2\sqrt{3}$

Put $x=2$ in $f\left(x\right)=x^2+x$ as follows:

$f\left(2\right)=(2{)}^2+2$

$=4+2$

$=6$

Now put $x=6$ in $g\left(x\right)=\sqrt{(x+6)}$

$g\left(6\right)=\sqrt{(6+6)}$

$=\sqrt{12}$

$=2\sqrt{3}$

Hence, $g\left(f\right(2\left)\right)=2\sqrt{3}$