Function Notation Calculator

Use * for multiplication, ^ for powers, √ for square root

What does f(x) mean?

f(x) represents a function named "f" with input variable "x". It shows the output value when x is the input. The letter f can be any letter (g, h, etc.).

How do I evaluate f(5)?

To evaluate f(5), replace every x in the function with 5, then simplify. For example, if f(x) = 2x + 3, then f(5) = 2(5) + 3 = 10 + 3 = 13.

Can I evaluate functions with negative numbers?

Yes! You can evaluate functions at any real number, including negative numbers and decimals. Just substitute the value and follow the order of operations carefully.

What is f(a + 1)?

f(a + 1) means substitute (a + 1) for every x in the function. For example, if f(x) = x², then f(a + 1) = (a + 1)² = a² + 2a + 1.

When is a function undefined?

A function is undefined when the operation is invalid, such as dividing by zero, taking the square root of a negative number, or taking the logarithm of zero or a negative number.

How do I enter powers and roots?

Use ^ for powers (x^2 for x²) and √ for square roots (√x). For other roots, use fractional powers like x^(1/3) for cube root.

What's the difference between f(x) and y?

f(x) and y are equivalent - both represent the output of the function. Function notation f(x) is more explicit about the input variable and is clearer when working with multiple functions.

Can I use this calculator for composite functions?

This calculator evaluates a single function at a specific value. For composite functions like f(g(x)), use our Function Composition Calculator.