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

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 $f \left(x\right) = 3 x + 4$, 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:

$y = \frac{1}{x}$

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 $x \ge 0$.

Hope that helps :)