Question

Find (f•g)(x) when f(x)=sqrt x+3/x and g(x)=sqrt x+3/2x

I'm a bit stuck on whether it is B or C, so if anyone can explain or confirm my answer it would help !!

Answer 1

`\textsf{C)} \quad (f \cdot g)(x)=(x+3)/(2x^2)`

Explanation:

Given functions:

`f(x)=(√(x+3))/(x)`

`g(x)=(√(x+3))/(2x)`

To find (f · g)(x), multiply the two functions:

`\begin{aligned}(f \cdot g)(x)&=f(x) \cdot g(x)\\\\&=(√(x+3))/(x) \cdot (√(x+3))/(2x)\\\\&=(√(x+3)√(x+3))/(x\cdot 2x)\end{aligned}`

`\textsf{Apply the radical rule:} \quad \sqrt{\vphantom{b}a}√(b)=√(ab)`

`\begin{aligned}&=(√((x+3)(x+3)))/(2x^2)\\\\&=(√((x+3)^2))/(2x^2)\end{aligned}`

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

`=(x+3)/(2x^2)`