Answer:
-1/2
Step-by-step explanation:
The relevant relationship is ...
f^-1'(x) = 1/f'(f^-1(x))
f^-1'(2) = 1/f'(f^-1(2)) = 1/f'(0) = 1/-2
f^-1'(2) = -1/2
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The attached graph shows the tangent lines at the relevant points. The red line is the tangent to f(0); the blue line is the tangent to f^-1(2).
The inverse function is the function reflected across the line y=x. So, too, for the tangent lines to the function. Each is a reflection of the other across the line y=x. For the purpose here, the tangent line is a suitable representation of the function at the point(s) of interest.
