Answer:

Step-by-step explanation:
Switch Sides

Subtract 2 From Both Sides

Simplify

Multiply Both Sides By -6

Simplify

Step-by-step explanation:
I can't see good the picture

will be increasing on the intervals where

and decreasing wherever

. Local extrema occur when

and the sign of

changes to either side of that point.

is positive when

is between -4 and some number between -2 and -1, and also 2 (exclusive) and 4, so you can estimate that

is increasing on the intervals [-4, -2] and (2, 4].

is negative when

is between some number between -2 and -1, up to some number less than 2. So

is decreasing on the interval [-1, 1].
You then have two possible cases for extrema occurring. The sign of

changes for some

between -2 and -1, and again to either side of

.
The inverse of this function would be f(x) =
.
You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.
f(x) =
- 6 ----> Switch f(x) and x
x =
- 6 ----> Add 6 to both sides
x + 6 =
-----> Take the logarithm of both sides in order to get the f(x) out of the exponent
Log(x + 6) = f(x)Log2 ----> Now divide both sides by Log2
= f(x) ----> And switch the order for formatting purposes.
f(x) = 
And that would be your new inverse function.
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