Operations with Functions

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does it mean to add two functions, f(x) and g(x)?

Back

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

Front

How do you subtract one function from another, f(x) - g(x)?

Back

To subtract one function from another, you find the difference of their outputs: (f - g)(x) = f(x) - g(x).

Front

What is function composition?

Back

Function composition is applying one function to the result of another: (f ∘ g)(x) = f(g(x)).

Front

How do you multiply two functions, f(x) and g(x)?

Back

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

Front

What is the quotient of two functions, f(x) and g(x)?

Back

The quotient of two functions is the division of their outputs: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

Given f(x) = x^2 and g(x) = 3x, find (f + g)(2).

Back

(f + g)(2) = f(2) + g(2) = 2^2 + 3(2) = 4 + 6 = 10.

Front

If f(x) = 2x + 1 and g(x) = x - 3, find (f - g)(1).

Back

(f - g)(1) = f(1) - g(1) = (2(1) + 1) - (1 - 3) = 3 - (-2) = 5.

Front

What is the result of (g ⋅ f)(x) if g(x) = 2x and f(x) = x + 1?

Back

(g ⋅ f)(x) = g(f(x)) = g(x + 1) = 2(x + 1) = 2x + 2.

Front

Find p(q(x)) if p(x) = x + 4 and q(x) = x^2.

Back

p(q(x)) = p(x^2) = x^2 + 4.