Unit 9 test review inverses and radical/cubic functions

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What is an inverse function?

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An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

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How can you determine if two functions are inverses of each other?

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You can determine if two functions are inverses by composing them. If f(g(x)) = x and g(f(x)) = x, then they are inverses.

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What is the horizontal line test?

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The horizontal line test is a method to determine if a function has an inverse. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

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What does it mean if a function passes the horizontal line test?

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If a function passes the horizontal line test, it means that it is one-to-one and has an inverse function.

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What is the composition of functions?

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The composition of functions is the process of applying one function to the results of another. It is denoted as (f ∘ g)(x) = f(g(x)).

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What is the significance of the composition of functions in determining inverses?

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The composition of functions helps verify if two functions are inverses. If f(g(x)) = x and g(f(x)) = x, then they are inverses.

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What is a radical function?

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A radical function is a function that contains a variable within a radical (square root, cube root, etc.). For example, f(x) = √x or f(x) = ∛x.

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What is a cubic function?

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A cubic function is a polynomial function of degree three, typically in the form f(x) = ax³ + bx² + cx + d, where a ≠ 0.

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How do you find the inverse of a function algebraically?

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To find the inverse of a function algebraically, swap the x and y in the equation and solve for y.

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

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The graphs of a function and its inverse are reflections of each other across the line y = x.