Time Remal This Question 1 pt 130120 6 complete Find the inv

Time Remal This Question: 1 pt 130120 (6 complete) Find the inverse function - of the tunction t Find the range of f and the domain and range off fox) - 4 sinx +1, Find the inverse, f1, of f f-1(x)-L (Use integers or tractions for any numbers in the expression ) The range of fo)is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression ) The domain oft(x) is (Type your answer in interval notation Use integers or fractions for anvy numbers in the expression.) The range of f-1(x)s Type your answer in interval notation. Use integers or fractions for any numbers in the expression) Enter your answer in each of the answer boxes PriSc Insert Deee

Solution

f(x) = y= 4 sin x +1

Switching x and y

x= 4 sin y +1

sin y=(x-1)/4

y=sin^-1((x-1)/4)

f^-1(x) = sin^-1((x-1)/4)

Range, when x=-pi/2, f(x)=4sin(-pi/2) +1=-4 +1=-3

when x=pi/2, f(x)=4sin(pi/2)+1=5

Range [-3,5]

Domain of f^-1(x) is same as range of f(x) which is [-3,5]

Range of f^-1(x) is same as domain of f(x) which is [-pi/2, pi/2]