What is the inverse of $$f(x) = x$$ ?

The inverse is $$f^{-1}(x) = x$$ .

Given the points (1, 4) and (4, 6) on $$f(x)$$ , what points are on $$f^{-1}(x)$$ ?

The points on $$f^{-1}(x)$$ are (4, 1) and (6, 4).

What is the condition for two functions to be inverses?

For two functions to be inverses, they must satisfy $$f(g(x)) = x$$ and $$g(f(x)) = x$$ .

How can you verify if two functions are inverses?

To verify if two functions are inverses, check if $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all $$x$$ in their domains.

What is the inverse of the function $$f(x) = 2x + 3$$ ?

The inverse is $$f^{-1}(x) = \frac{x - 3}{2}$$ .

What does it mean if two functions are not reflected over $$y = x$$ ?

If two functions are not reflected over $$y = x$$ , they are not inverse functions.

If $$f(x)$$ and $$g(x)$$ are inverse functions, what can be said about their outputs?

If $$f(x) = y$$ , then $$g(y) = x$$ .

What is the significance of the point (0, 0) in inverse functions?

The point (0, 0) is significant because it is where the function and its inverse intersect, indicating that $$f(0) = 0$$ and $$g(0) = 0$$ .

2.8 Inverse Functions 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 algebraically?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What does it mean for two functions to be inverses of each other?

Back

5.

FLASHCARD QUESTION

Front

What is the graphical representation of inverse functions?

Back

6.

FLASHCARD QUESTION

Front

If a function is not one-to-one, what can be said about its inverse?

Back

If a function is not one-to-one, it does not have an inverse that is also a function.

7.

FLASHCARD QUESTION

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

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

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