Question

F(x) = 3x + 1; g(x) = 5x - 1 find f/g. (f/g)(x) = quantity five x minus one divided by three x plus one.; domain {x|x ≠ - one over three. } (f/g)(x) = quantity three x plus one divided by five x minus one; domain {x|x ≠ - one over three. } (f/g)(x) = quantity five x minus one divided by three x plus one.; domain {x|x ≠ one over five. } (f/g)(x) = quantity three x plus one divided by five x minus one.; domain {x|x ≠ one over five. }

Answer 1

Given

$f(x)=3x+1\\g(x)=5x-1$

Find

$\dfrac{f}{g}(x)$

The domain of (f/g)(x).

Solution

Substitute for f(x) and g(x) in the desired relatinon.

$\dfrac{f}{g}(x)=\dfrac{f(x)}{g(x)}=\dfrac{3x+1}{5x-1}$

The domain must exclude the value of x that makes the denominator equal to zero.

$5x-1=0\\5x=1\qquad\text{add 1}\\x=\frac{1}{5}\qquad\text{divide by 5}$

The domain must exclude x=1/5.

This matches the last choice.