Question

1. find the composition of the function.

$f(x) = x^4$ and $g(x) = \sqrt{x}$ find $f(g(x))$.
$\circ x^6$
$\circ x^{\frac{1}{2}}$
$\circ x^3$
$\circ x^{\frac{3}{2}}$

Explanation:

Step1: Rewrite $g(x)$ as power form

$g(x)=\sqrt{x}=x^{\frac{1}{2}}$

Step2: Substitute $g(x)$ into $f(x)$

$f(g(x))=(x^{\frac{1}{2}})^{\frac{1}{4}}$

Step3: Apply exponent power rule

$(x^a)^b=x^{a \cdot b}$, so $f(g(x))=x^{\frac{1}{2} \times \frac{1}{4}}=x^{\frac{1}{8}}$

Answer:

$\boldsymbol{x^{\frac{1}{8}}}$ (matches the first option)