Why not just use the | character? It should be on your keyboard. Also, note that |-4(x + 3)| + 1 = |4(x + 3)| + 1.Coco12 said:Homework Statement
Y=abs -4(x+3) +1
Note: the 1 is outside the absolute value
No, you're way off. What happened to the absolute values? When you switch x and y, you should still have both x and y, but in different places. What happened to y here?Coco12 said:Homework Equations
Switch y and x
The Attempt at a Solution
So you subtract the 1 to bring it to the other side
After that do I put: x+1= -4(x+3)
And x+1= 4(x+3)
Am I doing this right??
The only functions that have inverses are those that are one-to-one. Is your function one-to-one?Coco12 said:What should be the two equations that u get?
Why is +1 now appearing on the left side?Coco12 said:Opps.. I meant to put x+1=-4(y+3) and so on for the other equation
No it's not. "Bringing the 1 over" is not a valid operation. When you started, there was a +1 term on the right side. How do you get rid of it?Coco12 said:The function is not one to one. I'm just trying to determine what the equations for the inverse of the absolute function is. I brought the 1 over from the other side now is just wondering what to do for the stuff inside the absolute value . Do I just take the positive version of it then solve and then the negative version and solve? Is my work above correct?
If you mean y - 1 = |-4(x + 3)|, then yes.Coco12 said:I meant to say that it would be x-1=|-4(x+3)|
Since it isn't one-to-one, you can't just assume that it is.Coco12 said:Where do I go from here assuming that it is one to one?
No, this is incorrect. For example, y = x2 is not one-to-one, so it does not have an inverse that is a function.Coco12 said:From my understanding a function does not have to be to one to be an inverse.
That's an outcome of a function being one-to-one, but it isn't the definition. Your book should have a definition of what it means for a function to be one-to-one, and several examples, including at least one where the function is not one-to-one, and what you need to do to find an inverse.Coco12 said:One to one simply means that both the function and it's inverse are functions.
Coco12 said:I'm trying to find the equation for the inverse
The inverse of an absolute value function is a function that undoes the effect of the original absolute value function. In other words, it takes the output of the absolute value function and returns the original input value.
To determine the inverse of an absolute value function, you switch the roles of x and y and solve for y. This will result in an equation that represents the inverse function.
The domain and range of the inverse of an absolute value function are the same as the original absolute value function. The domain is all real numbers and the range is also all real numbers, but it is reflected across the x-axis.
No, the inverse of an absolute value function cannot be negative. The absolute value function always returns a positive value, so the inverse function will also return a positive value.
The graph of an inverse of an absolute value function will be a reflection of the original function across the line y = x. This means that any points on the original function will have their x and y coordinates swapped on the inverse function.