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

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

Find the inverse of the function $$f(x) = \frac{3x - 15}{2}$$ .

$$f^{-1}(x) = \frac{15 + 2x}{3}$$ .

Find the inverse of the function $$h(x) = -\frac{2}{x - 1} - 3$$ .

$$h^{-1}(x) = \frac{2}{-x - 3} + 1$$ .

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

True, because f(g(x)) = x and g(f(x)) = x.

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

$$f^{-1}(x) = \frac{x + 5}{3}$$ .

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

Two functions are inverses if their compositions yield the identity function: f(f^{-1}(x)) = x and f^{-1}(f(x)) = x.

What is the graphical representation of a function and its inverse?

The graph of a function and its inverse are symmetric with respect to the line y = x.

How can you verify if two functions are inverses?

You can verify by checking if f(g(x)) = x and g(f(x)) = x for all x in the domain.

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

Finding the inverse of a function can help solve problems where you need to determine the original input from a given output.

Practice #29 - Finding Inverses of Functions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of the inverse of a function?

Back

The inverse of a function f(x) is a function f^{-1}(x) such that f(f^{-1}(x)) = x for all x in the domain of f^{-1}.

Tags

CCSS.HSF-BF.B.4A

2.

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 variables in the equation and solve for y.

Tags

CCSS.HSF-BF.B.4A

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

4.

FLASHCARD QUESTION

Front

Back

The inverse is not a function because it fails the horizontal line test.

5.

FLASHCARD QUESTION

Front

What is the horizontal line test?

Back

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

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

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