Composition and Inverse Functions Flashcard

Front

What are inverse functions?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

How can you determine if two functions are inverses of each other?

Back

To check if f(x) and g(x) are inverses, compute f(g(x)) and g(f(x)). If both equal x, they are inverses.

Front

What is the vertical line test?

Back

A graph represents a function if and only if no vertical line intersects the graph at more than one point.

Front

If f(x) passes through (a, b), what points does f^-1(x) pass through?

Back

f^-1(x) passes through (b, a).

Front

Given f(x) = 3x + 10, what is f(1)?

Back

f(1) = 3(1) + 10 = 13.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted f(g(x)), is applying g first and then f to the result.

Front

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

Back

f(g(2)) = f(2 + 3) = f(5) = 2(5) = 10.

Front

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

Back

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

Front

If f(x) = x^2, is f(x) one-to-one?

Back

No, f(x) = x^2 is not one-to-one because it fails the horizontal line test.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.