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1.6, #10. Determine if this is a one-to-one function: 
The  term
makes this suspicious right away. It means that we have a parabola which
opens downward. |
We know that a one-to-one function can't have any type of symmetry with respect to a vertical line. This is exactly what results from an equation such this equation. |
| Graphing the function can confirm our suspicions. A graph of this funciton is shown at right. |  |
| We can also use some algebra to confirm our suspicions. Lets say we set the funciton equal to -20. The question is: Is there more than 1 value for x which will give this value for f(x)? |
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| Clearly in all 3 views, there is more than 1 value for x that gives the same value for f(x). Therefore this function is not one-to-one. |
1.6, #30. Find an explicit formula for the inverse of 
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First, substitute y in place of the f(x) notation. |
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Swap the x and y variables. |
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Solve for y. Square both sides, set equation equal to zero, use quadratic
formula to solve for y.
Return to f(x) notation. |
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We have found the inverse. |
1.6, #50. Solve this equation for x: 
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Add 7 to both sides of the equation.
Take the natural log of both sides of the equation. Subtract three from both sides of the equation. Divide both sides of the equation by two. Calculate an approximate answer using a calculator. |
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