Function Notation & Operations

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically using symbols like f(x) to denote the output of a function f for a given input x.

Front

How do you add two functions?

Back

To add two functions f(x) and g(x), you combine their outputs: (f + g)(x) = f(x) + g(x).

Front

What is the formula for multiplying two functions?

Back

To multiply two functions f(x) and g(x), you multiply their outputs: (f * g)(x) = f(x) * g(x).

Front

What does f(2) mean?

Back

f(2) represents the output of the function f when the input is 2.

Front

How do you find (f + g)(x) for f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1?

Back

(f + g)(x) = (3x^2 + 7x) + (2x^2 - x - 1) = 5x^2 + 6x - 1.

Front

What is the value of g(-4) if g(x) = 3 - x?

Back

g(-4) = 3 - (-4) = 3 + 4 = 7.

Front

How do you calculate (f * g)(x) for f(x) = 4x + 1 and g(x) = 4x - 3?

Back

(f * g)(x) = (4x + 1)(4x - 3) = 16x^2 - 8x - 3.

Front

What is the result of (f * g)(x) if f(x) = 3 and g(x) = -2x + 5?

Back

(f * g)(x) = 3 * (-2x + 5) = -6x + 15.

Front

How do you evaluate (f + g)(2) for f(x) = 3x^2 + 1 and g(x) = 4x + 5?

Back

(f + g)(2) = f(2) + g(2) = (3(2)^2 + 1) + (4(2) + 5) = 26.

Front

What is the difference between f(x) and g(x)?

Back

f(x) and g(x) are two different functions that can be defined by different expressions or formulas.