Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = 5x and g(x) = 2x - 1, what is f(g(x))?

Back

f(g(x)) = f(2x - 1) = 5(2x - 1) = 10x - 5.

Front

How do you evaluate f(-1) for f(x) = 2x² + 5x - 17?

Back

Substituting -1 into the function: f(-1) = 2(-1)² + 5(-1) - 17 = 2 - 5 - 17 = -20.

Front

What is the result of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

g(5) = 5 - 2 = 3; then f(g(5)) = f(3) = 3(3) + 10 = 19.

Front

What does (f ° f)(-2) mean for f(x) = 2x² - 1?

Back

(f ° f)(-2) means to apply f twice: f(-2) = 2(-2)² - 1 = 8 - 1 = 7; then f(7) = 2(7)² - 1 = 97.

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is (g∘h)(x)?

Back

(g∘h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

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

Back

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

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input, denoted as I(x) = x.

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 and solve for y.

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.