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. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(g(x)) for given functions f and g?

Back

To find f(g(x)), substitute g(x) into the function f. This means you take the output of g(x) and use it as the input for f.

Front

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

Back

First, calculate g(2) = 3(2) + 1 = 7. Then, calculate f(7) = 2(7) = 14. So, f(g(2)) = 14.

Front

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

Back

First, calculate f(1) = 1^2 = 1. Then, calculate g(1) = 2(1) + 3 = 5. So, g(f(1)) = 5.

Front

What is the formula for the composition of two linear functions?

Back

If f(x) = ax + b and g(x) = cx + d, then the composition f(g(x)) = a(cx + d) + b = acx + (ad + b).

Front

How do you evaluate f(g(0)) for f(x) = 3x + 3 and g(x) = -4x + 1?

Back

First, calculate g(0) = -4(0) + 1 = 1. Then, calculate f(1) = 3(1) + 3 = 6. So, f(g(0)) = 6.

Front

What is the significance of the order of composition in functions?

Back

The order of composition matters because f(g(x)) is generally not equal to g(f(x)). The output of one function becomes the input of the other, affecting the final result.

Front

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

Back

g(f(x)) = g(x + 2) = (x + 2)^2 + 3 = x^2 + 4x + 4 + 3 = x^2 + 4x + 7.

Front

What is the output of f(g(x)) if f(x) = 3x and g(x) = 3x^2 - 2?

Back

f(g(x)) = f(3x^2 - 2) = 3(3x^2 - 2) = 9x^2 - 6.

Front

How do you find the value of a composition of functions at a specific point?

Back

To find the value of a composition of functions at a specific point, first evaluate the inner function at that point, then use that result as the input for the outer function.