Operations on Functions

Front

What is the definition of function addition?

Back

Function addition is the operation of adding two functions, defined as (f + g)(x) = f(x) + g(x) for all x in the domain of both functions.

Tags

CCSS.HSF-BF.A.1B

Front

What is the definition of function subtraction?

Back

Function subtraction is the operation of subtracting one function from another, defined as (f - g)(x) = f(x) - g(x) for all x in the domain of both functions.

Tags

CCSS.HSF-BF.A.1B

Front

What is the definition of function composition?

Back

Function composition is the operation of applying one function to the result of another, defined as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

What is the result of (f + g)(2) if f(x) = 3x^2 and g(x) = 4x + 5?

Back

(f + g)(2) = f(2) + g(2) = 3(2^2) + (4(2) + 5) = 12 + 13 = 25.

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

g(1) = 2(1) + 1 = 3, so f(g(1)) = f(3) = 3^2 = 9.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for (f - g)(x) when f(x) = 3x^2 - 4 and g(x) = x^2 - 8x + 4?

Back

(f - g)(x) = (3x^2 - 4) - (x^2 - 8x + 4) = 2x^2 + 8x - 8.

Tags

CCSS.HSF-BF.A.1B

Front

What is the value of f(g(0)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

What is the definition of 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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.