00:02
Given the function f of x equals negative absolute value x minus 1 minus 2, we're going to determine the inverse of this function and then take a look at the function and the inverse functions domain and range.
00:15
So first we're going to rewrite this as y equals negative absolute value of x minus 1 minus 2.
00:21
And to find the inverse of a function, we switch around the x and the y.
00:25
So we're going to get x equals negative absolute value y minus 1 minus 2.
00:33
And now we're going to re -solve for y.
00:35
Add two to both sides.
00:37
We get x plus 2 equals negative absolute value of y minus 1.
00:43
I'm going to multiply both sides by negative 1.
00:49
On the right -hand side, we get the absolute value of y minus 1.
00:53
And on the left, we need to distribute that negative 1.
00:55
So we get negative x minus 2.
00:58
So we have negative x minus 2 equals the absolute value of y minus 1.
01:05
And now what that means for us is, remember, anything inside this absolute value sign can be positive or negative, and then we would take the absolute value of it.
01:13
So this means that negative x minus 2 equals y minus 1 or negative x minus 2, negative of that equals y minus 1.
01:26
On the left hand one, i'm going to add one to both sides.
01:31
We get negative x minus 1 equals y.
01:34
On this left hand one, i'm going to distribute the negative.
01:37
We get x plus 2 equals y.
01:39
Y minus one add one to both sides we get x plus three equals y so our function f of x equals the absolute negative absolute value of x minus one minus two and the inverse function is negative x minus one or x plus three so let's take a look at what this means for its domain and range so i'm going to rewrite this over here so that we have it handy.
02:18
Our function f of x equals negative absolute value of x minus 1, minus 2, and the inverse function of x equals negative x minus 1 and x plus 3.
02:59
So now let's take a look at if we were to graph these.
03:02
So an absolute value function is a v -shaped...