2.3-Composition Of Functions

Front

What is the composition of functions?

Back

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

Front

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

Back

g(2) = 3(2) + 4 = 10.

Front

What is the notation for the composition of functions?

Back

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

Front

If f(x) = x^2 - 2, what is f(3)?

Back

f(3) = 3^2 - 2 = 7.

Front

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

Back

f(g(3)) = f(3 - 4) = f(-1) = 2(-1) + 1 = -1.

Front

If h(x) = -3x, what is h(1)?

Back

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

Front

What is the value of f(g(h(3))) if f(x) = x^2 - 2, g(x) = x + 9, and h(x) = -3x?

Back

f(g(h(3))) = f(g(-9)) = f(-9 + 9) = f(0) = 0^2 - 2 = -2.

Front

If f(x) = 3x - 2, what is f(g(x)) if g(x) = x + 5?

Back

f(g(x)) = f(x + 5) = 3(x + 5) - 2 = 3x + 15 - 2 = 3x + 13.

Front

What is the composition of g(h(x)) if g(x) = 3x + 4 and h(x) = x - 1?

Back

g(h(x)) = g(x - 1) = 3(x - 1) + 4 = 3x - 3 + 4 = 3x + 1.

Front

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

Back

f(g(2)) = f(2(2)) = f(4) = 4^2 = 16.