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

To find the inverse, solve for $$x$$ : Start with $$y = 2x + 3$$ , then switch $$x$$ and $$y$$ : $$x = 2y + 3$$ . Solving gives $$f^{-1}(x) = \frac{x - 3}{2}$$ .

How do you find the inverse of a function algebraically?

To find the inverse, replace $$f(x)$$ with $$y$$ , swap $$x$$ and $$y$$ , and then solve for $$y$$ .

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.

If $$f(x) = x^2$$ , what is the inverse function?

The function $$f(x) = x^2$$ is not one-to-one over all real numbers. Its inverse, $$f^{-1}(x) = \text{sqrt}(x)$$ , is valid only for $$x >= 0$$ .

What is the inverse of the function $$f(x) = 3x - 5$$ ?

To find the inverse, set $$y = 3x - 5$$ , switch $$x$$ and $$y$$ , and solve: $$f^{-1}(x) = \frac{x + 5}{3}$$ .

What does it mean for a function to be one-to-one?

A function is one-to-one if it never assigns the same value to two different domain elements, ensuring that it has an inverse.

What is the significance of the range of a function in finding its inverse?

The range of the original function becomes the domain of the inverse function, and vice versa.

How can you verify if two functions are inverses using composition?

To verify, compute $$f(g(x))$$ and $$g(f(x))$$ . If both equal $$x$$ for all $$x$$ in the domain, they are inverses.

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

The inverse function is the same: $$f^{-1}(x) = \frac{1}{x}$$ , as it is its own inverse.

Inverse Functions Flashcards

Student preview

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

How do you determine if two functions are inverses?

Back

Tags

CCSS.HSF-BF.B.4B

3.

FLASHCARD QUESTION

Front

What is the domain restriction for the inverse function of a quadratic function?

Back

The domain of the original function must be restricted to ensure that it is one-to-one, typically by limiting it to either the left or right half of the parabola.

Tags

CCSS.HSF-BF.B.4D

4.

FLASHCARD QUESTION

Front

What is the notation for an inverse function?

Back

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

6.

FLASHCARD QUESTION

Front

What is the graphical representation of inverse functions?

Back

Tags

CCSS.HSF-BF.B.4C

7.

FLASHCARD QUESTION

Front

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

Back

At any point where the function and its inverse intersect, the slopes are reciprocals of each other.

Tags

CCSS.HSF-BF.B.4C

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