### Home > APCALC > Chapter 2 > Lesson 2.1.3 > Problem2-35

2-35.

Construct a composite function $k(x)$ using $f(x) =\sqrt { x }$ and $g(x) = \log(x)$ if $k(x) =\frac { 1 } { 2 }\log(x)$.

$\text{since }\sqrt{x}=x^{\frac{1}{2}}.$

$\text{log}\sqrt{x}=\text{ log}x^{\frac{1}{2}}$

Since $\text{log}x^a = a\text{log}{x}$ (power log of logarithms).

$\text{log}x^{\frac{1}{2}}={\frac{1}{2}}\text{ log}x$