What is the domain of the square root function $$f(x) = \\sqrt{x}$$ ?

The domain of the square root function is $$[0, \\infty)$$ .

What is the range of the cube root function $$f(x) = \\sqrt[3]{x}$$ ?

The range of the cube root function is all real numbers, or $$(-\\infty, \\infty)$$ .

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

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

What is the notation for the inverse of a function $$f(x)$$ ?

The inverse is denoted as $$f^{-1}(x)$$ .

What is the domain of the function $$f(x) = \\sqrt{x - 3}$$ ?

The domain is $$[3, \\infty)$$ .

How do you determine if two functions are inverses of each other?

Two functions $$f(x)$$ and $$g(x)$$ are inverses if $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all $$x$$ in their domains.

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

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

What is the effect of reflecting a function over the line $$y = x$$ ?

Reflecting a function over the line $$y = x$$ produces its inverse function.

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

The domain is $$(-\\infty, 0) \\cup (0, \\infty)$$ .

What is the range of the function $$f(x) = \\sqrt{x}$$ ?

The range is $$[0, \\infty)$$ .

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

The inverse is $$f^{-1}(x) = \\sqrt[3]{x}$$ .

Inverses of Root Functions

Flashcard

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Easy

•

CCSS

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

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is the definition of an inverse function?

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

How do you find the inverse of a function algebraically?

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is the graphical representation of an inverse function?

Back

Tags

CCSS.HSF-BF.B.4C

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4D

FLASHCARD QUESTION

Front

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

Back

The domain of a function is the range of its inverse, and vice versa.

Tags

CCSS.HSF-BF.B.4C

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