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 ≠ - one over three. (f/g)(x) = quantity three x plus one divi…

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 (f/g)(x) = quantity three x plus one divided by five x minus one; domain x ≠ - one over three. (f/g)(x) = quantity five x minus one divided by three x plus one.; domain x (f/g)(x) = quantity three x plus one divided by five x minus one.; domain x ≠ one over five.

Answer 1

Given

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

Find

`(f)/(g)(x)`

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

Solution

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

`(f)/(g)(x)=(f(x))/(g(x))=(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=(1)/(5)\qquad\text{divide by 5}`

The domain must exclude x=1/5.

This matches the last choice.