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

The inverse function is $$f^{-1}(x) = \text{log}_5(x)$$ .

What is the inverse of the function $$f(x) = -4x - 12$$ ?

The inverse function is $$f^{-1}(x) = -\frac{1}{4}x - 3$$ .

Given the function $$f(x) = 2x^2 + 3$$ for $$x \\geq 0$$ , what is its inverse?

The inverse function is $$f^{-1}(x) = \text{sqrt}igg(\frac{x - 3}{2}\bigg)$$ .

If a linear function is given by $$f(x) = 2x + 3$$ , what is its inverse function?

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

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.

How can you verify if two functions are inverses of each other?

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

What is the graphical representation of inverse functions?

The graphs of inverse functions are reflections over the line $$y = x$$ .

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

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

What is the inverse of the function $$f(x) = \text{log}_2(x)$$ ?

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

What is the significance of the horizontal line test?

The horizontal line test determines if a function is one-to-one, which is necessary for it to have an inverse.

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

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

Inverse Functions

Flashcard

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Mathematics

•

11th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-BF.B.4A, HSF-BF.B.4C, HSF-BF.B.4B

Standards-aligned

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FLASHCARD QUESTION

Front

What is an inverse function?

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

How do you find the inverse of a function algebraically?

Back

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CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

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CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

What is the inverse of an exponential function?

Back

The inverse of an exponential function is a logarithmic function.

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

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