Question

Find (f • g) (x) Assume x>0

Answer 1

`\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`