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

A function must be one-to-one (bijective) to have an inverse.

How can you determine if a function is one-to-one?

A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once.

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

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

What is the inverse of the function $$f(x) = x^2$$ for $$x \text{ in } [0, \text{∞})$$ ?

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

What is the composition of a function and its inverse?

The composition of a function and its inverse yields the identity function: $$f(f^{-1}(x)) = x$$ and $$f^{-1}(f(x)) = x$$ .

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

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

What is the significance of the inverse function in real-world applications?

Inverse functions are used in various applications, such as calculating the original value from a transformed value in finance, physics, and engineering.

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

To verify, check if $$f(f^{-1}(x)) = x$$ and $$f^{-1}(f(x)) = x$$ for all x in the domain.

Inverse Functions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the notation for an inverse function?

Back

2.

FLASHCARD QUESTION

Front

What is an inverse function?

Back

Tags

CCSS.HSF-BF.B.4A

3.

FLASHCARD QUESTION

Front

How do you find the inverse of a function algebraically?

Back

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

Tags

CCSS.HSF-BF.B.4A

4.

FLASHCARD QUESTION

Front

What is the relationship between a function and its inverse?

Back

Tags

CCSS.HSF-BF.B.4C

5.

FLASHCARD QUESTION

Front

What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.

Tags

CCSS.HSF-BF.B.4C

6.

FLASHCARD QUESTION

Front

What is the range of an inverse function?

Back

The range of the inverse function is the domain of the original function.

Tags

CCSS.HSF-BF.B.4C

7.

FLASHCARD QUESTION

Front

What is the graphical representation of an inverse function?

Back

Tags

CCSS.HSF-BF.B.4C

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