Evaluating 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 evaluate a composite function?

Back

To evaluate a composite function (f∘g)(x), first evaluate g(x) and then substitute that result into f.

Front

What is the notation for composite functions?

Back

The notation for composite functions is (f∘g)(x), which means f(g(x)).

Front

If f(x) = 2x + 3 and g(x) = x - 1, what is (f∘g)(2)?

Back

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

Front

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

Back

f(g(x)) means applying g first and then f, while g(f(x)) means applying f first and then g. They are generally not equal.

Front

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

Back

g(f(2)) = g(2^2) = g(4) = 3(4) = 12.

Front

What is the output of g(f(-10)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

g(f(-10)) = g(3(-10) + 10) = g(-20) = -20 - 2 = -22. (Note: The answer is None of these as per the question.)

Front

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

Back

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

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 result of (f∘g)(0) if f(x) = 3x + 10 and g(x) = x - 2?

Back

(f∘g)(0) = f(g(0)) = f(0 - 2) = f(-2) = 3(-2) + 10 = 4.