What is the first step in finding the inverse of $$f(x) = 2x + 3$$ ?

Replace $$f(x)$$ with $$y$$ to get $$y = 2x + 3$$ .

What points does the inverse function $$f^{-1}(x)$$ go through if $$f(x)$$ goes through (1, 4) and (4, 6)?

$$f^{-1}(x)$$ goes through (4, 1) and (6, 4).

What is the significance of switching $$x$$ and $$y$$ when finding an inverse?

Switching $$x$$ and $$y$$ allows you to express the output of the original function as the input of the inverse function.

What does it mean if two functions are not inverse functions?

If two functions do not satisfy the conditions $$f(g(x)) = x$$ and $$g(f(x)) = x$$ , they are not inverse functions.

What is the relationship between the domains and ranges of a function and its inverse?

The domain of the original function is the range of its inverse, and the range of the original function is the domain of its inverse.

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

To verify, check if $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all $$x$$ in the domain.

What is the inverse of the function $$f(x) = x^2$$ for $$x >= 0$$ ?

The inverse is $$f^{-1}(x) = \text{sqrt}(x)$$ for $$x >= 0$$ .

What happens to the graph of a function when you find its inverse?

The graph of the inverse function is a reflection of the original function's graph over the line $$y = x$$ .

What is the importance of the greatest common factor in finding inverses?

The greatest common factor is not directly related to finding inverses; it is more relevant in simplifying expressions or factoring.

Inverse Functions Review Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an inverse function?

Back

2.

FLASHCARD QUESTION

Front

How do you find the inverse of a function?

Back

3.

FLASHCARD QUESTION

Front

What does it mean for two functions to be inverse functions?

Back

4.

FLASHCARD QUESTION

Front

What is the graphical representation of inverse functions?

Back

5.

FLASHCARD QUESTION

Front

If a function passes the horizontal line test, what can be said about its inverse?

Back

If a function passes the horizontal line test, it is one-to-one, and its inverse will also be a function.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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