Inverse Functions (VCE SSCE Mathematical Methods): Quizzes

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Inverse functions
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For a function to have an inverse, what property must it have?

It must be one-to-one

What does the horizontal line test check?

If function is one-to-one

What does the notation f−1f^{-1} represent?

The inverse function

If ran f=[2,5]\text{ran } f = [2, 5], what is dom f−1\text{dom } f^{-1}?

[2,5][2, 5]

What does f∘f−1(x)f \circ f^{-1}(x) equal?

xx

How do you obtain the graph of f−1f^{-1} from the graph of ff?

Reflect across line y=xy = x

If point (3,7)(3, 7) is on graph of ff, which point is on graph of f−1f^{-1}?

(7,3)(7, 3)

What is the first step in Method 1 for finding an inverse?

Write y=f(x)y = f(x)

For h(x)=x2−2h(x) = x^2 - 2, x≥1x \geq 1, why is h−1(x)=x+2h^{-1}(x) = \sqrt{x+2} not −x+2-\sqrt{x+2}?

Range of h−1h^{-1} must be [1,∞)[1, \infty)

Where do graphs of ff and f−1f^{-1} intersect?

On line y=xy = x where f(x)=xf(x) = x

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Relations, Domain and Range

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Relations, Domain and Range

One-to-One Functions and Implied Domains

Piecewise-Defined Functions

Applying Function Notation

Set Notation and Sets of Numbers

Sums and Products of Functions

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Relations, Domain and Range

One-to-One Functions and Implied Domains

Piecewise-Defined Functions

Applying Function Notation

Set Notation and Sets of Numbers

Sums and Products of Functions

Composite Functions

Inverse Functions

Power Functions

Applications of Functions

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Power Functions

Applications of Functions

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