Composite Functions

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 the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the given value into the function's equation and simplify.

Front

If h(a) = 3 - 2a, what is h(-3)?

Back

h(-3) = 3 - 2(-3) = 3 + 6 = 9.

Front

What is the difference of two functions, (f - g)(x)?

Back

The difference of two functions is calculated by subtracting the second function from the first: (f - g)(x) = f(x) - g(x).

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f - g)(x).

Back

(f - g)(x) = (3x^2 + 7x) - (2x^2 - x - 1) = x^2 + 8x + 1.

Front

What is the process to find g(f(x))?

Back

To find g(f(x)), first calculate f(x) and then substitute that result into g(x).

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is g(f(-10))?

Back

g(f(-10)) = g(3(-10) + 10) = g(-20) = -20 - 2 = -22.

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, find g(f(x)).

Back

g(f(x)) = g(-3x + 7) = 2(-3x + 7)^2 - 8 = 18x^2 - 84x + 90.

Front

What is the process to find f(g(x))?

Back

To find f(g(x)), first calculate g(x) and then substitute that result into f(x).

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, find f(g(x)).

Back

f(g(x)) = f(2x^2 - 8) = -3(2x^2 - 8) + 7 = -6x^2 + 31.