What is the inverse of the function $$f(x) = \frac{3x + 10}{7}$$ ?

The inverse is $$f^{-1}(x) = \frac{7x - 10}{3}$$ .

How can you verify if two functions are inverses?

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

What is the significance of the line $$y = x$$ in relation to inverse functions?

The line $$y = x$$ serves as the line of reflection for the graphs of a function and its inverse.

What happens to the slopes of a function and its inverse?

The slopes of a function and its inverse are reciprocals of each other at corresponding points.

What is the inverse of a linear function?

For a linear function of the form $$f(x) = mx + b$$ , the inverse is $$f^{-1}(x) = \frac{x - b}{m}$$ .

Can a function have more than one inverse?

No, a function can have at most one inverse unless it is not one-to-one.

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 it has an inverse.

What is the inverse of the function represented by the table?

To find the inverse from a table, swap the input and output values.

Are the functions $$f(x) = 2x + 3$$ and $$g(x) = \frac{x - 3}{2}$$ inverses of each other?

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$ .

Review 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 an inverse function?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What does it mean if two functions are inverses of each other?

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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