state the domain of f(x) = (x+3)/(x-1)
anything goes except x cannot be 1, or else we are dividing by zero
so domain: set of real numbers, x not equal to 1
let hx and h be real numbers.
If f(x) =4x +3, which of the following is true and why:
1.f(x+h)=4x+3+h
2.f(x+h)=4x+4h+3
3.f(x+h)=4x+4h+6
To determine the domain of a function, we need to find the values of x for which the function is defined. In this case, the function is defined for all values of x except when the denominator of the function is zero.
So, to find the domain of f(x) = (x+3)/(x-1), we set the denominator x-1 equal to zero and solve for x:
x - 1 = 0
Adding 1 to both sides, we get:
x = 1
Therefore, the function is undefined when x = 1, as it would result in division by zero.
Hence, the domain of f(x) = (x+3)/(x-1) is all real numbers except x = 1. In interval notation, we could write the domain as (-infinity, 1) U (1, +infinity).