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

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

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

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

What is the importance of the horizontal line test?

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function does not have an inverse.

What does it mean if two functions are not inverses?

If two functions are not inverses, it means that composing them does not yield the identity function, i.e., @@f(g(x)) eq x $$ or $$ g(f(x)) eq x@@.

What is the inverse of the function $$f(x) = 3x - 12$$ ?

The inverse is $$f^{-1}(x) = \frac{x + 12}{3}$$ .

How do you graph the inverse of a function?

To graph the inverse, reflect the original function's graph across the line $$y = x$$ .

What is the domain of an inverse function?

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

What is the range of an inverse function?

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

What is a one-to-one function?

A one-to-one function is a function where each output is produced by exactly one input, ensuring that it has an inverse.

Verify Inverse Functions Flashcards

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15 questions

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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

What is the graphical representation of inverse functions?

Back

4.

FLASHCARD QUESTION

Front

What is the relationship between a function and its inverse?

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

How can you verify if two functions are inverses?

Back

7.

FLASHCARD QUESTION

Front

Back

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