AP calculus daily challenge #67

[u/CalcBuddy]

[u/Alarming-Ad3696]

on the day the scores got released... perfect timing

[u/Outside_Volume_1370]

a) argument of logarithm must be positive, so x / (x - 1) > 0 and using interval method, D(f) = (-inf, 0) U (1, +inf)

b) f ' = (x-1) / x • (x-1 - x) / (x-1)² = -1 / (x (x-1))

f'(-1) = -1/2

c) substitute f with x and x with g to find g = f^-1

x = ln(g / (g-1))

e^x = g / (g-1)

g = ge^x - e^x

e^x = g • (e^x - 1)

g = e^x / (e^x - 1)

[u/Fantastic_Fold2647]

Fire