What is the domain of #f(x)=3x+4#?

1 Answer
Sep 13, 2014

It's all real numbers.

The domain of any function is simply all the possible numbers you can input for #x# without violating the rules of math.

In the given function #f(x) = 3x + 4#, you can input any number for #x# without violating the rules of math, or blowing a hole through the earth's core. However, when you get more complex functions, like those with fractions and square roots, things become a bit more tricky.

For example, consider the function below:

#y = 1/x#

In this function, you can input every number except one number: zero. This is because it is against the rules of math to divide by zero. Hence, the domain of this function would be all reals except zero, or all non-zero numbers.

Similarly, in a square root function such as #y = sqrt(x)#, then we cannot have a negative number for x (its against the laws of math), so the domain would be all non-negative numbers, or #x >=0#.

Hope that helps :)