y=2x2+x212
y=2x2+12x−2
dxdy=(2)(2)x2−1+(12)(−2)x−2−1
dxdy=4x−24x−3
at the point x=2
dxdy=4(2)−(24)(2)−3
dxdy=12−824
dxdy=9
Hence the derivative of y=2x2+12/x2, when x=2 is
dxdy=9
Given that f(x)=y=−x−73 .
Interchanging x (domain) and y (range)
x=−y−73
Now making y the subject of the formula, we have
x(y−7)=−3
y−7=−x3
y=−x3+7
Hence the inverse function of the given function f(x)=y=−x−73 is
f−1(x)=−x3+7
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