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.
To find the function f/g, we need to divide the function f(x) by g(x).
So, f/g is given by: f(x)/g(x) = (4x + 3)/(4x - 5)
To simplify this expression, we can factor out a common factor of 4 in the numerator:
f(x)/g(x) = (4(x + 3/4))/(4x - 5)
The 4 in the numerator and denominator cancel out, leaving us with:
f(x)/g(x) = (x + 3/4)/(x - 5/4)
Now, to determine the domain of f/g, we need to identify any restrictions on the value of x that would result in division by zero.
In this case, the denominator (x - 5/4) should not be equal to zero. Thus, we cannot have x = 5/4.
Therefore, the domain of f/g is all real numbers except x = 5/4. In interval notation, the domain can be represented as (-∞, 5/4) ∪ (5/4, +∞).