Function Composition

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 of f and g is denoted as f(g(x)).

Front

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

Back

To evaluate f(g(x)), first calculate g(x) for a given x, then substitute that result into f(x).

Front

Given f(x) = x^2 + x, find f(2).

Back

f(2) = 2^2 + 2 = 4 + 2 = 6.

Front

Given g(x) = 3x + 1, find g(4).

Back

g(4) = 3(4) + 1 = 12 + 1 = 13.

Front

If f(x) = x^2 - 5x, what is f(4)?

Back

f(4) = 4^2 - 5(4) = 16 - 20 = -4.

Front

What is the result of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

f(g(4)) = f(13) = 13^2 + 13 = 169 + 13 = 182.

Front

If f(x) = 3x + 10 and g(x) = x - 2, find f(g(x)).

Back

f(g(x)) = f(x - 2) = 3(x - 2) + 10 = 3x - 6 + 10 = 3x + 4.

Front

What is 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 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.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if they produce the same output for every input in their common domain.