What does f(x) mean in math?

f(x) means the output of the function f for the input x. You read it “f of x”. It is the number the rule gives back when you put x in.

Is f(x) the same as y?

On a graph, yes: y = f(x). Writing f(x) names the function, so you can say f(4) or g(4) when there is more than one function.

f(2) means the output of f when the input is 2. Replace every x in the rule with 2 and work it out, or read it from a table or a graph.

How do you solve f(x) = a number?

Put the rule in place of f(x) and solve the equation. For f(x) = 3x − 1, the question f(x) = 11 becomes 3x − 1 = 11, which gives x = 4.

Part 2 of 10 · FunctionsSee the whole course

What does f(x) mean?

By The Pip team · October 23, 2026 · 5 min read

Short answer

f(x) is the output of the function f when the input is x. You read it “f of x”. The brackets do not mean multiply: f(4) means “put 4 into f”, not “f times 4”.

Read it out loud

Take the rule f(x) = 3x − 1. In words: “f of x equals three x minus one.”

f is the name of the function. It could be g or h, it is only a label, so you can tell several functions apart.
x is a stand-in for any input.
f(4) means: replace x with 4, then work it out.

Evaluate a function from its rule

“Evaluate” just means “find the output for this input”. Two steps:

Replace every x with the input, and put the input in brackets.
Work it out, multiplying before you subtract.

f(4) = 3(4) − 1 = 12 − 1 = 11
f(0) = 3(0) − 1 = 0 − 1 = −1
f(−2) = 3(−2) − 1 = −6 − 1 = −7

The brackets matter most when the input is negative. Without them, 3 − 2 − 1 would give the wrong answer.

Try it. Slide the input and watch the dot move along the line. Then switch to “Work backwards”.

Input x 4

f(4) = 3(4) − 1 = 11

Put 4 in, and 11 comes out. So f(4) = 11.

Read f(x) from a table

A table lists inputs and their outputs. This is the same function f(x) = 3x − 1:

x: 1, 2, 3, 4
f(x): 2, 5, 8, 11

To find f(2), find 2 in the x row and read the number under it: f(2) = 5. You never need the rule for that, only the table.

Read f(x) from a graph

On a graph, the input runs across and the output is how high the graph is. To read f(2): find 2 on the x-axis, go straight up to the graph, then look across to the y-axis. For this line you land on the point (2, 5), so f(2) = 5.

Work backwards: which input gives this output?

Sometimes you are given the output and asked for the input. “f(x) = 11” asks: which x gives 11?

3x − 1 = 11
3x = 12
x = 4

On the graph you do the trip the other way round: start at 11 on the y-axis, go across to the line, then drop straight down to the x-axis. You land on 4. This is the first time you solve an equation, and the idea comes back in our post on solving linear equations.

Watch it explained in under a minute

The same idea, narrated step by step. Square version for sharing: download the 1:1 video.

The five mistakes to avoid

Reading f(2) as “f times 2”. The brackets mean “put 2 in”.
Replacing only one x. If x appears twice in the rule, replace both.
Dropping the brackets for a negative input: f(−2) = 3(−2) − 1, not 3 − 2 − 1.
Mixing up the question. f(4) gives you an output (11). f(x) = 11 asks for an input (4).
Thinking the letter has to be f. A function can be called g, h, or anything else.

Try it yourself

Let f(x) = 2x + 5. Tap a question to see the answer.

1. Find f(3)

f(3) = 2(3) + 5 = 6 + 5 = 11.

2. Find f(−4)

f(−4) = 2(−4) + 5 = −8 + 5 = −3.

3. Which x gives f(x) = 9?

2x + 5 = 9, so 2x = 4 and x = 2.

Where f(x) fits in

f(x) is the language of every later topic: lines, curves and waves are all written as f(x). If the idea of a function is new, start with what a function is. Next in this course: domain and range, which says which inputs a function accepts and which outputs it gives back.