The formula C − 5 sF 2 32d, where F > 2459.67, 9 expresses the Celsius temperature C as a function of the Fahrenheit temperat
1 answer:
Answer:
a) The inverse of the function is
b) The domain of the inverse function is C>1348.70.
Step-by-step explanation:
Given : The formula , where
express the Celsius temperature C as a function of the Fahrenheit temperature F.
To find : a) A formula for the inverse function and interpret it.
b) What is the domain of the inverse function?
Solution :
a) The formula
The inverse function of the given formula is the value of F.
Taking F to one side and rest term to other side,
Therefore, The inverse of the function is
i.e. Fahrenheit temperature F as a function of the Celsius temperature C.
b) The domain of the inverse function.
We have given,
Substituting in the formula,
The domain of the inverse function is C>1348.70.
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- x = ±√3, and they are actual solutions
- x = 3, but it is an extraneous solution
Step-by-step explanation:
The method often recommended for solving an equation of this sort is to multiply by the product of the denominators, then solve the resulting polynomial equation. When you do that, you get ...
... x^2(6x -18) = (2x -6)(9)
... 6x^2(x -3) -18(x -3) = 0
...6(x -3)(x^2 -3) = 0
... x = 3, x = ±√3
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Alternatively, you can subtract the right side of the equation and collect terms to get ...
... x^2/(2(x -3)) - 9/(6(x -3)) = 0
... (1/2)(x^2 -3)/(x -3) = 0
Here, the solution will be values of x that make the numerator zero:
... x = ±√3
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So, the actual solutions are x = ±3, and x = 3 is an extraneous solution. The value x=3 is actually excluded from the domain of the original equation, because the equation is undefined at that point.
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<em>Comment on the graph</em>
For the graph, we have rewritten the equation so it is of the form f(x)=0. The graphing program is able to highlight zero crossings, so this is a convenient form. When the equation is multiplied as described above, the resulting cubic has an extra zero-crossing at x=3 (blue curve). This is the extraneous solution.
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Step-by-step explanation:
The standard charge includes an initial fee and plus an addditional fee for each mile driven and is given by:
The insurance charge is given by:
So, the total charge C will be the sum of the standard charge S and the insurance charge I:
Substitute:
Rearrange:
Add:
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