Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ° g)(x) = f(g(x)).

Front

How do you evaluate (f ° g)(-1)?

Back

To evaluate (f ° g)(-1), first find g(-1), then substitute that result into f.

Front

What does f[g(5)] represent?

Back

f[g(5)] means to first evaluate g at 5, and then use that result as the input for the function f.

Front

If f(x) = 2x and g(x) = x² + 3, what is f(g(x))?

Back

f(g(x)) = f(x² + 3) = 2(x² + 3) = 2x² + 6.

Front

What is the output of h(f(-2)) if f(x) = 2x?

Back

First, calculate f(-2) = 2(-2) = -4, then find h(-4).

Front

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

Back

To find f(g(x)), substitute g(x) into f. This means replacing x in f with g(x).

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g. They are generally not equal.

Front

What is the domain of the composition of functions?

Back

The domain of (f ° g) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

What is the range of a composition of functions?

Back

The range of (f ° g) is the set of all possible outputs f(g(x)) for x in the domain of g.

Front

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

Back

f(g(x)) = f(x + 4) = 3(x + 4) - 2 = 3x + 12 - 2 = 3x + 10.