1.16 Inverse functions

We are playing the function game. Every time you give Christian a number, he doubles it and subtracts six.

• A

  If you give Christian a ten, what will he give you back?

• B

  If you give Christian an $x$ , what will he give you back?

• C

  What number would you give Christian, that would make him give you a 0?

• D

  What number would you give Christian, that would make him give you a ten?

• E

  What number would you give Christian, that would make him give you an $x$ ?
  Try to follow the process you used to answer part (d).

A television set dropped from the top of a 300' building falls according to the equation: $h(t)=\text{300}-\text{16}{t}^2$

$h(t)=\text{300}-\text{16}{t}^2$

where $t$ is the amount of time that has passed since it was dropped (measured in seconds), and $h$ is the height of the television set above ground (measured in feet).

• A

  Where is the television set after 0 seconds have elapsed?

• B

  Where is the television set after 2 seconds have elapsed?

• C

  A man is watching out of the window of the first floor, 20' above ground. At what time does the television set go flying by?

• D

  At what time does the television reach the ground?

• E

  Find a general formula $t(h)$ that can be used to quickly and easily answer all questions like (c) and (d).

$y=x+5$

• Inverse function:
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$y=x+6$

• Inverse function:
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$y=\mathrm{3x}$

• Inverse function:
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$y=\frac{x}{4}$

• Inverse function:
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$y=\mathrm{3x}+\text{12}$

• Inverse function:
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$y=\frac{\text{100}}{x}$

• Inverse function:
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$y=\frac{\mathrm{2x}+3}{7}$

• Inverse function:
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$y=x^2$

• Inverse function:
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$y=2^x$

• Inverse function:
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