F.1 Intervention (Function Composition)

Front

What is function composition?

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

Given f(x) = -9x + 3 and g(x) = x^4, find (f ∘ g)(x).

Back

(f ∘ g)(x) = -9x^4 + 3.

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = 2x - 1, g(x) = 3x, and h(x) = x^2 + 1, what is h(g(f(5)))?

Back

h(g(f(5))) = 169.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for finding (f ∘ g)(x) when f(x) and g(x) are given?

Back

(f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = -3x + 7 and g(x) = 2x^2 - 8, what is (f ∘ g)(3)?

Back

(f ∘ g)(3) = -23.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(h(2))) = 35.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(-3)) = -19.

Tags

CCSS.HSF-BF.A.1C

Front

What is the output of a function when the input is zero?

Back

The output of a function at zero is found by substituting x = 0 into the function's equation.

Tags

CCSS.HSF.IF.A.2

Front

What is the significance of the order of functions in composition?

Back

The order of functions in composition matters; (f ∘ g)(x) is not necessarily equal to (g ∘ f)(x).

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate a composite function step by step?

Back

To evaluate a composite function, first evaluate the innermost function, then substitute that result into the next function, and continue until all functions are evaluated.

Tags

CCSS.HSF-BF.A.1C