2.3-Composition Of Functions

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)).

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.

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

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

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

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

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

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

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

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