Flashcardizz Inverses

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If the function is represented as f(x), its inverse is denoted as f^{-1}(x). For a function to have an inverse, it must be one-to-one (each output is produced by exactly one input).

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, follow these steps: 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^{-1}(x).

Front

If a function contains the point (a, b), what point must be included on its inverse?

Back

The inverse function must include the point (b, a). This is because the roles of the input and output are reversed in the inverse.

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

Yes, they are inverses because g(f(x)) = x and f(g(x)) = x.

Front

What is the inverse of the function f(x) = (x - 6)^2?

Back

The inverse is f^{-1}(x) = \\sqrt{x} + 6.

Front

What does it mean for two functions to be inverses of one another?

Back

Two functions are inverses if applying one function followed by the other returns the original input. Mathematically, f(f^{-1}(x)) = x and f^{-1}(f(x)) = x.

Front

How can you tell if two graphs represent inverse functions?

Back

If the graphs are symmetric with respect to the line y = x, they are likely inverses of each other.

Front

What is the importance of one-to-one functions in finding inverses?

Back

Only one-to-one functions have inverses because they ensure that each output corresponds to exactly one input, preventing ambiguity.

Front

What is the inverse of the function f(x) = 3x - 5?

Back

The inverse is f^{-1}(x) = (x + 5)/3.