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

The inverse is $$f^{-1}(x) = \text{log}_3(x)$$ .

Convert the exponential equation $$7^3 = 343$$ to logarithmic form.

The logarithmic form is $$\text{log}_7(343) = 3$$ .

What is the inverse function of $$y = (x - 8)^3$$ ?

The inverse function is $$y = \text{cube root}(x) + 8$$ .

What is the inverse function of $$y = \text{cube root}(2x) + 7$$ ?

The inverse function is $$y = \frac{(x - 7)^3}{2}$$ .

How do you find the inverse of a function algebraically?

To find the inverse, swap the x and y in the equation and solve for y.

What is the domain of the inverse function if the original function has a range of [0, ∞)?

The domain of the inverse function will be [0, ∞) if the original function's range is [0, ∞).

What is the logarithmic identity for changing the base of a logarithm?

The identity is $$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any base k.

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

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

If $$f(x) = 2x + 3$$ , what is $$f^{-1}(x)$$ ?

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

What is the value of $$\text{log}_2(8)$$ ?

The value is 3, since $$2^3 = 8$$ .

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

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

Explain the concept of one-to-one functions in relation to inverses.

A function must be one-to-one (bijective) to have an inverse, meaning each output is produced by exactly one input.

Inverse Functions Review (Units 5 and 6) Flashcards

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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The value of x is 36.

5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

Front

Define an inverse function.

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between a function and its inverse?

Back

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