Function Operations and compositions

Front

What is function addition?

Back

Function addition is the operation of adding two functions together. If f(x) and g(x) are two functions, then (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is function subtraction?

Back

Function subtraction is the operation of subtracting one function from another. If f(x) and g(x) are two functions, then (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is function multiplication?

Back

Function multiplication is the operation of multiplying two functions together. If f(x) and g(x) are two functions, then (f * g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is function composition?

Back

Function composition is the operation of applying one function to the result of another function. If f(x) and g(x) are two functions, then (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find (f + g)(x) for f(x) = 2x and g(x) = 3x + 1?

Back

(f + g)(x) = f(x) + g(x) = 2x + (3x + 1) = 5x + 1.

Tags

CCSS.HSF-BF.A.1B

Front

How do you find (f - g)(x) for f(x) = x^2 + 3 and g(x) = x + 1?

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

What is the result of f(g(2)) if f(x) = x^2 and g(x) = 2x + 1?

Back

g(2) = 2(2) + 1 = 5; f(g(2)) = f(5) = 5^2 = 25.

Tags

CCSS.HSF-BF.A.1C

Front

What is the value of (f * g)(1) if f(x) = x + 2 and g(x) = x^2?

Back

(f * g)(1) = f(1) * g(1) = (1 + 2) * (1^2) = 3 * 1 = 3.

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

What is the composition of functions f(x) = x + 1 and g(x) = 2x?

Back

(f ∘ g)(x) = f(g(x)) = f(2x) = 2x + 1.

Tags

CCSS.HSF-BF.A.1C