Question

3/ Find the inverse of the function f(x) and state the domain and the range of f1. f(x) = 3 cos (5x) + 2 for 0 sxsn/5

Answer 1

y = f(x) = 360$ (5w) #2 for 0<x<T For x in the given range, ye for decreases morbonically with increase in t because cosine function decreases in gios) quaclrant (QI). Ymaximum = ymax = f(0) = 3603(0)42 = 3(0)42 and Yminimum = youin = f(") - 3 Cs(3.9) +2 = 3 Cos()+2 = 3 (-1)+2 = -342 from 0 : y-2 = 3 Cos(5x) * cos(5x) = you a 3 5x = Cost (2-2) 3 x= 1 / Cos (12) - Changing the reanable on RH. S f ein 9 from y tox, f(x) = f 65'(*- *) for -|5X55 daran innene function, gel

y = f(x) = 360$ (5w) #2 for 0<x<T For x in the given range, ye for decreases morbonically with increase in t because cosine function decreases in gios) quaclrant (QI). Ymaximum = ymax = f(0) = 3603(0)42 = 3(0)42 and Yminimum = youin = f(") - 3 Cs(3.9) +2 = 3 Cos()+2 = 3 (-1)+2 = -342 from 0 : y-2 = 3 Cos(5x) * cos(5x) = you a 3 5x = Cost (2-2) 3 x= 1 / Cos (12) - Changing the reanable on RH. S f ein 9 from y tox, f(x) = f 65'(*- *) for -|5X55 daran innene function, gel

For X:-1, f'(x) = f Cos" (-1-2) . : - Cos? (-1) = . We restrict the value of arccos function to Qi (5 m fer ve arguments & Corresponding to x 64,2), to QI? for the argument corresponoling to . XE(2, 5] and Cos (0) = 114 for x = 2. solusasugustele . Then, for x= a, f(x) = 60; (O) = 5 d = o and for x=5, f623 65'(?)- $ 65 3). cóco 5.0 - 0. Ausway earth clemain : Hisx55 and range : 1.7