Question

What is the equation for the inverse of y = 1/2 Sin x?
Is the answer y=2 Arcsin x?

Answer 1

Switch x and y in the original equation, and solve for y.

Answer 2

Start with the first step and show it.
Write the original equation and switch the variables.

Answer 3

hint:
we can write this:
\[\Large y = \frac{1}{2}\sin x \Rightarrow \sin x = 2y\]

Answer 4

y=2 Arcsin x ?

Answer 5

To answer your question, the answer is no, that is not the answer.
How about paying attention to what I am trying to show you.
I am guiding you through the process of finding an inverse function.
Start with the original function.
Now switch the variables, what do you get?

Answer 6

x=1/2 Sin y

Answer 7

Arcsin x=1/2 y

Answer 8

Great. (The first of the two lines above.)
Now you need to solve for y.
Switch sides to have the y on the left side.
Then multiply both sides by 2.

Answer 9

I got 2 Arcsin x=y

Answer 10

One step at a time.

This is good.

\(x = \dfrac{1}{2} \sin y\)

Now switch sides.
Then multiply both sides by 2.

Answer 11

switch sides?

Answer 12

Switch the left and right sides of the equation so you have the y variable on the left side.

Answer 13

\(x = \dfrac{1}{2} \sin y\)

\(\dfrac{1}{2} \sin y = x\)

Answer 14

Since you have 1/2 multiplying sin y, and you want to solve for sin y then for y, multiply both sides by 2.

Answer 15

sin y=2x

Answer 16

Great.
Now finally, you take the inverse sin, or the arcsin.

Answer 17

y=arcsin 2x

Answer 18

Exactly.
Now you got it right.
Good job!

Answer 19

thanx

Answer 20

I like the way you explain it, instead of giving a straight answer.

Answer 21

Now I know how to solve these kinds of problems.

Answer 22

The process is always the same to find an inverse function:
Step 1. Write the original equation.
If the function is given in function notation, \(f(x) = ...\) , then replace f(x) with y.
Step 2. Switch x and y.
Step 3. Solve for y.
Step 4. If you need function notation, replace y with \(f^{-1}(x) \)

Answer 23

You're welcome.