2.3-Composition Of Functions

Front

Define composition of functions.

Back

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

Front

What is the notation for the composition of functions?

Back

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

Front

Back

First, find g(3): g(3) = 3^2 = 9. Then, find f(9): f(9) = 2(9) + 1 = 19. So, f(g(3)) = 19.

Front

Back

First, find g(-5): g(-5) = -3(-5) + 2 = 15 + 2 = 17. Then, find f(17): f(17) = -2(17) + 3 = -34 + 3 = -31.

Front

Back

g(-3) = -3(-3) + 2 = 9 + 2 = 11.

Front

Back

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

Front

Back

First, find h(3): h(3) = -3(3) = -9. Then, g(-9) = -9 + 9 = 0. Finally, f(0) = 0^2 - 2 = -2.

Front

Back

f(g(x)) = f(x + 5) = 3(x + 5) - 16 = 3x + 15 - 16 = 3x - 1.

Front

Back

f(0) = -2(0) + 3 = 3.

Front

Define the term 'domain' in the context of functions.

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.