If $$y = x^2$$ , what is the inverse function?

The inverse function is $$y = \text{sqrt}(x)$$ , considering only the non-negative square root.

How do you find the inverse of the function $$y = (x + 5)^2 - 3$$ ?

1. Swap x and y: $$x = (y + 5)^2 - 3$$ . 2. Add 3 to both sides: $$x + 3 = (y + 5)^2$$ . 3. Take the square root: $$\text{sqrt}(x + 3) = y + 5$$ . 4. Subtract 5: $$y = \text{sqrt}(x + 3) - 5$$ .

What is the domain of the function $$y = \text{sqrt}(x)$$ ?

The domain is all non-negative real numbers, i.e., $$x \geq 0$$ .

What is the range of the function $$y = x^2$$ ?

The range is all non-negative real numbers, i.e., $$y \geq 0$$ .

If a function is increasing, what can be said about its inverse?

The inverse function will also be increasing.

What is the graphical relationship between a function and its inverse?

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

What does it mean if two functions are inverses?

If two functions are inverses, then applying one function after the other returns the original input.

How do you verify if two functions are inverses?

To verify, check if $$f(g(x)) = x$$ and $$g(f(x)) = x$$ for all x in the domain.

What is the inverse of the function $$y = 2x + 3$$ ?

The inverse is $$y = \frac{x - 3}{2}$$ .

What is the effect of a negative sign in front of a function when finding its inverse?

A negative sign reflects the function across the x-axis, affecting the inverse accordingly.

What is the importance of the domain when finding inverses?

The domain of the original function must be considered to ensure the inverse is also a function.

Square Root & Quadratic Inverses Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a square root?

Back

A square root of a number is a value that, when multiplied by itself, gives the original number.

2.

FLASHCARD QUESTION

Front

What does it mean to find the inverse of a function?

Back

Finding the inverse of a function means switching the x's and y's in the equation.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse 'undo' each other; applying one after the other returns the original value.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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