Function Operations and Compositions

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition (f ° g)(x) is defined as f(g(x)).

Front

How do you find (f ° g)(x) if f(x) = x - 5 and g(x) = 3x^2 - 1?

Back

(f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.

Front

What is the formula for multiplying two functions f(x) and g(x)?

Back

The product of two functions is given by (f * g)(x) = f(x) * g(x).

Front

If f(x) = 4x + 8 and g(x) = x + 3, what is f(x) * g(x)?

Back

f(x) * g(x) = (4x + 8)(x + 3) = 4x^2 + 20x + 24.

Front

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

Back

The sum of two functions is given by (f + g)(x) = f(x) + g(x).

Front

When f(x) = 9 - 3x and g(x) = 5x - 7, how do you find (f + g)(x)?

Back

(f + g)(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

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

Back

The difference of two functions is given by (f - g)(x) = f(x) - g(x).

Front

If f(x) = 3x - 1 and g(x) = x^2 + 2, how do you find (f ° g)(x)?

Back

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

Front

What is the result of (f - g)(x) if f(x) = 5x^2 + 3x and g(x) = 8x^2 + 16x?

Back

(f - g)(x) = (5x^2 + 3x) - (8x^2 + 16x) = -3x^2 - 13x.

Front

Define the term 'function'.

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, called the domain.