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

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

What is the inverse of $$f(x) = \sqrt{x} + 3$$ ?

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

How do you find the inverse of $$f(x) = \sqrt{x} - 4$$ ?

The inverse is $$f^{-1}(x) = (x + 4)^2$$ .

What is the relationship between a function and its inverse?

A function and its inverse are reflections of each other across the line $$y = x$$ .

What is the domain of a square root function?

The domain of a square root function is the set of all non-negative real numbers, as the square root of a negative number is not defined in the real number system.

What is the range of a quadratic function?

The range of a quadratic function depends on the direction of the parabola: if it opens upwards, the range is $$[k, \infty)$$ ; if it opens downwards, the range is $$(-\infty, k]$$ , where $$k$$ is the y-coordinate of the vertex.

What is the effect of the coefficient $$a$$ in a quadratic function?

The coefficient $$a$$ determines the direction of the parabola (upward if $$a > 0$$ , downward if $$a

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

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

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

quadratic and square root inverses

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

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

Standards-aligned

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FLASHCARD QUESTION

Front

What is a quadratic function?

Back

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

FLASHCARD QUESTION

Front

What is the inverse of a function?

Back

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