Continuity and DifferentiabilityHard
Question
Let ef(x) = ln x. If g(x) is the inverse function of f(x), then g′(x) equals to:
Options
A.ex
B.ex + x
C.ex + ex
D.ex + ln x
Solution
ef(x) = ln x
∵ f-1 (x) = g(x)
x = eef(x)
⇒ g(x) = f-1(x) = eex
⇒ g′(x) = eex .ex = eex + x
∵ f-1 (x) = g(x)
x = eef(x)
⇒ g(x) = f-1(x) = eex
⇒ g′(x) = eex .ex = eex + x
Create a free account to view solution
View Solution FreeMore Continuity and Differentiability Questions
If t = ae x / (x − b), then equals to -...If x = y ln(xy), then equals-...If y = sin−1 + sec−1 , then dy/dx equals -...The function f(x) = is not defined at x = 0. The value which should be assigned to f at x = 0, so that it is continuous ...Let f(x) = where [x] denotes the greatest integer function. Then -...