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

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Mathematics

Imani Li

3 May, 06:47

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

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Diana Becker · 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