Expand the logarithm $$\text{ln}igg(\frac{5\text{sqrt}(x)}{y}igg)$$

$$\text{ln}igg(5igg) + \frac{1}{2}\text{ln}(x) - \text{ln}(y)$$

How do you find the inverse of a function algebraically?

To find the inverse, replace $$f(x)$$ with $$y$$ , swap $$x$$ and $$y$$ , and solve for $$y$$ .

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

The range of $$y=x^2$$ is $$[0, \text{∞})$$ .

What is the property of logarithms that allows expansion?

The properties include: $$\text{log}_b(mn) = \text{log}_b(m) + \text{log}_b(n)$$ and $$\text{log}_bigg(\frac{m}{n}igg) = \text{log}_b(m) - \text{log}_b(n)$$ .

What is the end behavior of polynomial functions of even degree?

For even degree polynomials, as @@x ightarrow ext{∞} $$ and $$ x ightarrow - ext{∞} $$, the function approaches the same limit (either both to $$ ext{∞} $$ or both to $$ - ext{∞}@@).

What is the significance of the restricted domain in finding inverses?

A restricted domain ensures that the function is one-to-one, allowing for a valid inverse to be found.

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

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

How do you determine the domain of a composite function?

The domain of a composite function $$f(g(x))$$ is the set of all $$x$$ such that $$g(x)$$ is in the domain of $$f$$ .

What is the definition of a polynomial function?

A polynomial function is a function that can be expressed in the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , where $$a_n, a_{n-1}, ..., a_0$$ are constants and $$n$$ is a non-negative integer.

Precalc. AB Semester Final Part 2

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Mathematics

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12th Grade

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Hard

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

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