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

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

What is the graphical representation of an inverse function?

The graph of an inverse function is obtained by reflecting the graph of the original function across the line $$y = x$$ .

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; no horizontal line intersects the graph more than once.

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

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

What is the notation for the inverse of a function $$g$$ ?

The notation for the inverse of a function $$g$$ is $$g^{-1}$$ .

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

Provide an example of a function and its inverse.

Example: Function: $$f(x) = 3x - 5$$ ; Inverse: $$f^{-1}(x) = \frac{x + 5}{3}$$ .

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

Inverse functions are used in various applications, such as calculating time from speed and distance, or finding original values in data analysis.

Inverse Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the notation for an inverse function?

Back

2.

FLASHCARD QUESTION

Front

Define an inverse function.

Back

3.

FLASHCARD QUESTION

Front

What is the relationship between a function and its inverse?

Back

4.

FLASHCARD QUESTION

Front

How do you find the inverse of a function algebraically?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

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.

7.

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.

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