inverse function?

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suppose g is the inverse function of f and f(4)=5, f'(4)= 2/3. find g'(5)

2006-10-25 03:25:03 · 4 answers · asked by Lauren K 1 in Science & Mathematics ➔ Mathematics

dy/dx = 1/(dx/dy), so g'(5) should be the reciprocal of the value of f' at the point where f = 5, meaning that g'(5) = 1/f'(4) = 3/2.

2006-10-25 03:29:43 · answer #1 · answered by DavidK93 7 · 0⤊ 0⤋

g`(x)=1/f`(g(x))

g`(5)=1/f`(g(5)) = 1/f`(4) = 3/2

2006-10-25 03:35:28 · answer #2 · answered by bruinfan 7 · 0⤊ 0⤋

by using the rule: g'(x)=1/(f'(g(x))
and since f(4)=5 than g(5)=4
so the answer is 3/2

2006-10-25 03:49:38 · answer #3 · answered by Anonymous · 0⤊ 0⤋

If g is only defined at two points, it is not continuous and its derivative is undefined.

2006-10-25 03:31:44 · answer #4 · answered by fcas80 7 · 0⤊ 0⤋