Inverse Functions
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| One-to-one functions pass both the ______ & ______ test. | Vertical & Horizontal line test.
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| Determine if this function is a one-to-one function. Explain why. f= { (4, 2,), (3, 1), (-6, 12), (-2, 0) } | f is one-to-one since each y-value corresponds to only one x-value
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| Determine if this function is a one-to-one function. Explain why. h= { (0, 0), (1, -2), (3, 0), (2, 4) } | h is not one-to-one because the y-value 0 in (0, 0) and (3, 0) corresponds to different x-values.
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| What is a horizontal line test? | If every horizontal line intersects the graph of a function at most once, then the function is a one-to-one function.
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| Find the inverse. f= { (0, 2), (-3, 6), (1, -7), (6, 4) } | f^-1 = { (2, 0), (6, -3, (-7, 1), (4, 6) }
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| Find the equation of the inverse of f(x) = 2x^2-3 | Step 1. Replace f(x) with y; y = 2x^2-3.
Step 2. Switch y & x; x= 2y^2-3
Step 3. Solve for y; x+3=2y^2-3+3, (x+3)/2=(2y^2)/2, √((x+3)/2)= √(y^2), y = √((x+3)/2)
Step 4. Replace y with f(x); f(x) = √((x+3)/2)
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| How do you describe the graphs of f(x) and f^-1(x). | The graphs are mirror images of each other or symmetric about the line y = x.
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| Is this an example of an one-to-one function? Explain. http://library.thinkquest.org/20991/media/alg2_vertlinetest.gif | No, because the same y values correspond to different x values and thus does not pass the horizontal line test.
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| Is this an example of an one-to-one function? Explain. http://fomcarynthompson.files.wordpress.com/2013/02/graph20x3.gif | Yes, because each y-value corresponds to only one x-value
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| (f o f^-1) (x) = ?? | x
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