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natima [27]
2 years ago
13

For the function find f-1(x)

Mathematics
2 answers:
Svetach [21]2 years ago
8 0
The answer is C. i know because i looked it up
Mkey [24]2 years ago
6 0

since you know that to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solve for "y".

\stackrel{f(x)}{y}=\sqrt[3]{\cfrac{x+6}{2}}\implies \stackrel{\textit{quick switcheroo}}{x=\sqrt[3]{\cfrac{y+6}{2}}}\implies \stackrel{\textit{cubing both sides}}{x^3=\cfrac{y+6}{2}} \\\\\\ 2x^3=y+6\implies 2x^3-6=\stackrel{f^{-1}(x)}{y}

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Recall that y = f(x) since both are outputs of a function.

If k = 2, then f(x) = 2 leads to y = 2 being a horizontal line drawn through 2 on the y axis. This horizontal line only crosses the cubic curve at one spot. The same can be said if k = 0 and k = -2. So we can rule out choices A,B,C.

On the other hand, if k = -3, then f(x) = -3 has three different solutions. This is because the horizontal line through -3 on the y axis crosses the cubic at 3 different intersection points.

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