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.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3