Function Operations and compositions

Front

What is function subtraction?

Back

Function subtraction involves taking two functions, f(x) and g(x), and creating a new function (f - g)(x) = f(x) - g(x).

Front

How do you find (f + g)(x) for two functions f(x) and g(x)?

Back

To find (f + g)(x), you add the outputs of the two functions: (f + g)(x) = f(x) + g(x).

Front

What is the result of f(x) - g(x) if f(x) = x^2 + 1 and g(x) = 2x - 5?

Back

The result is f(x) - g(x) = x^2 - 2x + 6.

Front

What is function multiplication?

Back

Function multiplication involves multiplying the outputs of two functions: (f * g)(x) = f(x) * g(x).

Front

How do you find f(g(x))?

Back

To find f(g(x)), substitute g(x) into the function f(x).

Front

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

Back

The result is f(g(0)) = 4.

Front

What is the formula for finding (f * g)(x) if f(x) = x^3 - 3x and g(x) = -4x + 1?

Back

The formula is (f * g)(x) = f(x) * g(x) = -4x^4 + x^3 + 12x^2 - 3x.

Front

What does f(n) + g(n) represent?

Back

f(n) + g(n) represents the sum of the outputs of the two functions evaluated at n.

Front

What is the result of f(n) + g(n) if f(n) = 2n + 1 and g(n) = 3n?

Back

The result is f(n) + g(n) = 5n + 1.

Front

Define function composition.

Back

Function composition is the process of applying one function to the results of another function: (f ∘ g)(x) = f(g(x)).