Composite Functions Review

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find the value of a composite function?

Back

To find the value of a composite function f(g(x)), first evaluate g(x) for the given x, then substitute that result into f.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^-1(x) that reverses the effect of f. If f(a) = b, then f^-1(b) = a.

Front

How do you find the inverse of a quadratic function?

Back

To find the inverse of a quadratic function, first express y = f(x), then solve for x in terms of y, and finally swap x and y.

Front

What is the significance of the domain and range in composite functions?

Back

The domain of the composite function f(g(x)) is determined by the domain of g(x) and the range of g(x) must be within the domain of f(x).

Front

Given f(x) = 2x^2 - 3x + 1, how do you find f(5)?

Back

Substitute x = 5 into the function: f(5) = 2(5)^2 - 3(5) + 1 = 50 - 15 + 1 = 36.

Front

What is the process to evaluate f(g(3))?

Back

First, calculate g(3), then substitute that result into f to find f(g(3)).

Front

If g(x) = -3x, what is g(f(x)) when f(x) = x^2 + 2?

Back

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

Front

What is the formula for finding g(f(x)) if g(x) = x^2 - 1?

Back

To find g(f(x)), substitute f(x) into g: g(f(x)) = (f(x))^2 - 1.

Front

How do you determine the output of f(g(3)) if f(x) = 3x + 2?

Back

First, find g(3), then substitute that value into f: f(g(3)) = f(value of g(3)).