Step by step
The question
Question: find the domain of f(x) = 2x + 1.
f(x) = 2x + 1
The domain is all the x's we can put in.
domain = the x's that can go in
1 Look for a problem
Two things can go wrong: a 0 at the bottom of a fraction, or a negative number under a square root.
÷ 0: not allowed
√ of a negative: not allowed
Here there is no fraction with x at the bottom, and no square root.
So any number can go in: the domain is all real numbers.
domain : all real numbers
2 Check
Let's check with a negative number: −3.
It works fine.
f(−3) = 2(−3) + 1 = −6 + 1 = −5
Let's look back.
First: look for a problem.
Last: check.
Answer
domain : all real numbers