Find (f • g) (x) Assume x>0

Question 1

Question 2

Answer:

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

Explanation:

Given:

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

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

$\textsf{Apply radical rule} \quad √(a)√(b)=√(ab):$

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

Rewrite 100 as 10²:

$\implies (f \cdot g)(x)=√(10^2x^2)$

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

$\implies (f \cdot g)(x)= √((10x)^2)$

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

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

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