Question

If $f\left(x\right)=$ $\sqrt{x}$ and $g\left(x\right)=$ $\sqrt{x^2+4}$, calculate the value of $f\left(g\right(2\left)\right)$.

• A. $0$
• B. $1.41$
• C. $1.68$
• D. $2.45$
• E. $2.83$

Answer 1

The correct option is C $1.68$

Given functions are $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=\sqrt{x^2+4}$.

Now $g\left(2\right)=\sqrt{2^2+4}=2\sqrt{2}$

Then $f\left(g\right(2\left)\right)=\sqrt{g\left(2\right)}=\sqrt{2\sqrt{2}}=2^{3/4}=1.681$