Composition and Inverse Functions (2A Review)

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you denote the composition of functions a and b?

Back

The composition of functions a and b is denoted as b(a(x)).

Front

What is the value of a(5) if f(5) = 13?

Back

The value of a(5) is 13.

Front

What is the value of b(5) if b(5) = 24?

Back

The value of b(5) is 24.

Front

How do you solve b(a(5))?

Back

To solve b(a(5)), first find a(5), then substitute that value into b.

Front

What is the significance of inverse functions in composition?

Back

Inverse functions reverse the effect of the original function. If f is a function and f^(-1) is its inverse, then f(f^(-1)(x)) = x.

Front

What is the formula for finding the inverse of a function?

Back

To find the inverse of a function, swap the x and y in the equation and solve for y.

Front

What is the output of the composite function b(a(x))?

Back

The output of the composite function b(a(x)) is found by first calculating a(x) and then applying b to that result.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are related such that if f(a) = b, then f^(-1)(b) = a.

Front

How do you evaluate a composite function at a specific value?

Back

To evaluate a composite function at a specific value, substitute the value into the innermost function first, then use that result in the outer function.