Question

If g is an increasing function such that g(2)=8 and g'(2)=5 calculate (g^-1)'(8)

Answer 1

The inverse of a function is the reflection of it across the line y=x. If (2, 8) is on the graph of g(x), then (8, 2) is on the graph of its inverse. If the slope of g(2) is 5, then the slope of (g^-1)(8) is 1/5, the reciprocal of g'(2).

... (g^-1)(8) = 1/5