Composition of Functions (evaluate)

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f ° g)(x) = f(g(x)).

Front

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

Back

To evaluate g(f(x)), first find the value of f(x) and then substitute that value into g.

Front

What does f(f(x)) represent?

Back

f(f(x)) represents the function f applied to the result of f(x), indicating a repeated application of the function.

Front

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

Back

f(3) = 2(3) + 1 = 7.

Front

If g(x) = x^2, what is g(f(-2)) if f(-2) = -2?

Back

g(f(-2)) = g(-2) = (-2)^2 = 4.

Front

What is the notation for function composition?

Back

The notation for function composition is f ° g, which means f(g(x)).

Front

If f(x) = x + 1 and g(x) = 2x, what is (f ° g)(-1)?

Back

(f ° g)(-1) = f(g(-1)) = f(2(-1)) = f(-2) = -2 + 1 = -1.

Front

What is the value of h(f(-1)) if f(-1) = -1 and h(x) = x - 3?

Back

h(f(-1)) = h(-1) = -1 - 3 = -4.

Front

How do you find (f ° g)(x)?

Back

To find (f ° g)(x), compute g(x) first, then substitute that result into f.

Front

If f(x) = x^2 and g(x) = x + 1, what is (f ° g)(2)?

Back

(f ° g)(2) = f(g(2)) = f(2 + 1) = f(3) = 3^2 = 9.