Pregunta
4.1 - Verifying Invers…
4.1 - Verifying Inverses (Linear and Cubic)
Use the theorem on inverse functions to pro
and sketch the graphs of f and g on the same
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4.1 - Verifying Inverses (Linear and Cubic)
Use the theorem on inverse functions to pro
and sketch the graphs of f and g on the same
Ask by Whittaker Gibbs. in the United States
Jan 23,2025
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Respuesta verificada por el tutor
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All four pairs of functions
and
are inverses of each other. Their graphs are reflections of each other across the line
.
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Bonus Knowledge
To verify that two functions are inverses, check if
and
for each pair. For instance, with
and
, if you substitute
into
, you’ll find that
demonstrating they are indeed inverses. Sketching the graphs will reveal that they are reflections across the line
, showcasing their inverse relationship beautifully!
Have fun experimenting with transformations! For
and
, applying the cube function “undoes” the cube root, resulting in the identity function. When graphing these, make sure to plot points around critical values, such as the origin and any intercepts. You’ll see how each function complements the other, creating an intriguing symmetry!
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