Graph the inverse circular function by hand, given f(x) = 3sin(2x) ;-pi/4 ≤ ≤pi/4
a) Find the inverse function ^-1()
b) Find the range of f
c) Find the domain and range of ^-1()
d) Graph ^-1().

Part a)

a) The given function is

We let

Interchange x and y.

Solve for y;

Part b) The range of f(x) refers to y-values for which f(x) exists.

The range of f(x) is

This is because the function is within y=-3 and y=3.

c) The range of

is

The domain is -3≤x≤3

This is because the domain and range of a function and its inverse swaps.

Part d) The graph is shown in the attachment.

okay wait before i answer, is this for your points on a graph?