If $$f(x) = 2x + 3$$ , what is $$f^{-1}(x)$$ ?

To find the inverse, swap $$x$$ and $$y$$ : 1. Start with $$y = 2x + 3$$ . 2. Swap: $$x = 2y + 3$$ . 3. Solve for $$y$$ : $$y = \frac{x - 3}{2}$$ . Thus, $$f^{-1}(x) = \frac{x - 3}{2}$$ .

If $$f(2) = 5$$ , what is $$f^{-1}(5)$$ ?

If $$f(2) = 5$$ , then by definition of inverse functions, $$f^{-1}(5) = 2$$ .

How do you find the inverse of a function algebraically?

1. Replace $$f(x)$$ with $$y$$ . 2. Swap $$x$$ and $$y$$ . 3. Solve for $$y$$ . 4. Replace $$y$$ with $$f^{-1}(x)$$ .

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

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

What is the inverse of $$f(x) = 3x - 4$$ ?

To find the inverse: 1. Set $$y = 3x - 4$$ . 2. Swap: $$x = 3y - 4$$ . 3. Solve for $$y$$ : $$y = \frac{x + 4}{3}$$ . Thus, $$f^{-1}(x) = \frac{x + 4}{3}$$ .

What is the significance of the point (a, b) in relation to inverse functions?

If $$(a, b)$$ is a point on the graph of $$f$$ , then $$(b, a)$$ is a point on the graph of $$f^{-1}$$ .

What is the condition for a function to have an inverse?

A function must be one-to-one (bijective) to have an inverse, meaning it passes the horizontal line test.

If $$f(x) = x^3$$ , what is $$f^{-1}(x)$$ ?

The inverse is $$f^{-1}(x) = \text{cube root}(x) = x^{1/3}$$ .

What is the inverse of $$f(x) = \frac{1}{x}$$ ?

The inverse is $$f^{-1}(x) = \frac{1}{x}$$ , meaning it is its own inverse.

How do you verify if two functions are inverses?

To verify, check if $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all $$x$$ in their respective domains.

Inverse Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an inverse function?

Back

Tags

CCSS.HSF-BF.B.4A

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

3.

FLASHCARD QUESTION

Front

What does it mean for two functions to be inverses?

Back

Tags

CCSS.HSF-BF.B.4B

4.

FLASHCARD QUESTION

Front

How can you graph inverse functions?

Back

Tags

CCSS.HSF-BF.B.4C

5.

FLASHCARD QUESTION

Front

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

Back

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

Tags

CCSS.HSF-BF.B.4C

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4C

7.

FLASHCARD QUESTION

Front

What is the notation for an inverse function?

Back

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