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.

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.

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)).

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.

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.

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.

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.

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.

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.

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.