Question

Find (f • g) (x) Assume x>0

Answer 1

Answer:

$\textsf{B.} \quad (f \cdot g)(x)=10x$

Step-by-step explanation:

Given:

$\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}$

$\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}$

$\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:$

$\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}$

Rewrite 100 as 10²:

$\implies (f \cdot g)(x)=\sqrt{10^2x^2}$

$\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:$

$\implies (f \cdot g)(x)= \sqrt{(10x)^2}$

$\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:$

$\implies (f \cdot g)(x)=10x$