REVIEW of Operations & Composition of functions

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(g(0)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

First, find g(0): g(0) = 0 - 2 = -2. Then, find f(-2): f(-2) = 3(-2) + 10 = 4.

Front

What is the value of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

First, find g(4): g(4) = 3(4) + 1 = 13. Then, find f(13): f(13) = 13^2 + 13 = 182.

Front

How do you evaluate q(p(-2)) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

First, find p(-2): p(-2) = 3(-2) + 4 = -2. Then, find q(-2): q(-2) = 2(-2)^2 = 8.

Front

What is the result of (f - g)(2) if f(x) = 3x + 4 and g(x) = 2x^2?

Back

First, find f(2): f(2) = 3(2) + 4 = 10. Then, find g(2): g(2) = 2(2)^2 = 8. Therefore, (f - g)(2) = 10 - 8 = 2.

Front

What is the simplified form of (f/g)(x) if f(x) = 2x^2 + 12x and g(x) = x^2 - 3x - 54?

Back

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. It can be represented as f(x), where x is the input.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if (f ∘ g)(x) = x and (g ∘ f)(x) = x for all x in the domain of f and g.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function f(x), swap x and y in the equation, then solve for y. The result is the inverse function, denoted as f^(-1)(x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.