Composition of Functions

Front

What is a 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)).

Front

If f(x) = 2x + 3, what is f(1)?

Back

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

Front

If g(x) = -3x - 4, what is g(2)?

Back

g(2) = -3(2) - 4 = -10.

Front

What is the notation for function composition?

Back

The notation for function composition is f(g(x)), which means you apply g first and then apply f to the result.

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(g(1))?

Back

g(1) = 5(1) - 7 = -2; f(-2) = 9 - 3(-2) = 15.

Front

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

Back

g(3) = -3(3) - 4 = -13; f(-13) = 2(-13) + 3 = -23.

Front

If f(x) = 2x + 3 and g(x) = -3x - 4, find f(g(-4)).

Back

g(-4) = -3(-4) - 4 = 8; f(8) = 2(8) + 3 = 19.

Front

What is the product of two functions f(x) and g(x)?

Back

The product of two functions f(x) and g(x) is denoted as f(x) * g(x).

Front

If f(x) = 2x + 3 and g(x) = -3x - 4, find f(x) * g(x).

Back

f(x) * g(x) = (2x + 3)(-3x - 4) = -6x^2 - 17x - 12.

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions f(x) and g(x) is denoted as f(x) + g(x).