Find the requested function and state its domain:
f(x)= 4x+3 g(x)=4x-5 Find f/g and its domain.
So I did 4x+3/4x-5, so the 4x's cancel out and 3/-5 is left. So my answer is 3/-5. Is this correct Now I just need to find the domain which I am not to sure about.
Nooooo!
You can't cancel out 4x cuz it's not multiply.
f/g = (4x+3)/(4x+5) (you can't simplify it)
Domain: all real number except x = -5/4
To find f/g, you correctly simplified the expression to 3/-5. However, to determine the domain of f/g, we need to consider any restrictions on the variables involved.
In this case, the division operation introduces a restriction. Division by zero is undefined, so the expression f/g is not defined when the denominator (4x-5) equals zero. Therefore, we need to find the values of x that make the denominator zero and exclude them from the domain.
To find these values, we set the denominator equal to zero and solve for x:
4x - 5 = 0
Adding 5 to both sides:
4x = 5
Dividing both sides by 4:
x = 5/4
So, x = 5/4 is the value that makes the denominator zero, which means it should be excluded from the domain.
Therefore, the domain of f/g is all real numbers except x = 5/4. In interval notation, it can be expressed as (-∞, 5/4) U (5/4, +∞).