If $$f(x) = x^2$$ , what is the restriction on the domain for its inverse?

The domain of $$f(x) = x^2$$ must be restricted to $$x \geq 0$$ to ensure that the inverse function is also a function.

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

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

Given the points (1,3), (2,4), (6,8), what are the inverse points?

The inverse points are (3,1), (4,2), (8,6).

What is the domain of the inverse function of $$f(x) = \frac{x^2 - 8}{-4}$$ ?

The domain of the inverse function is $$(-\infty, 2]$$ .

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

A function is one-to-one if it never takes the same value twice; that is, $$f(a) = f(b)$$ implies $$a = b$$ .

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 significance 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 is not one-to-one.

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

The inverse function is $$f^{-1}(x) = x^2$$ , with the restriction that $$x \geq 0$$ .

What happens to the domain of a function when finding its inverse?

The domain of the original function becomes the range of the inverse function.

If $$g(x) = f^{-1}(x)$$ , what is the relationship between $$g(x)$$ and $$f(x)$$ ?

The function $$g(x)$$ is the inverse of $$f(x)$$ , meaning that $$g(f(x)) = x$$ and $$f(g(x)) = x$$ .

Restriction on Domain of 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 can you determine if two functions are inverses of each other?

Back

3.

FLASHCARD QUESTION

Front

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

Back

4.

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.

5.

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.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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