Question

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

Answer 1

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 :)