We actually don't need to do any computation. By definition, the inverse function
changes the role of input and output. So, if a function f maps x onto y, the inverse function maps y onto x.
You have to think like this: if the function makes a step further, the inverse function makes that same step back.
This means that the composition
is always the identity function
. In fact,

So, for every function, you have

Answer:

Step-by-step explanation:
The parent function denotes the simplest function (free from any horizontal/vertical stretch/compression) that represents a family of functions. In this case the term 1/4 indicates a horizontal stretch and should be removed to find the parent function of
. From here we're in simplest form, since
or others represent a completely different family of functions and cannot be obtained from horizontal/vertical stretches/compressions.
The greatest common factor is 3x². The rest doesn't factor.
21x³y² -3x²y +75x⁴ = 3x²(7xy² -y +25x²)
Let's make an equation where x is the number of gallons and y will be the overall price.
2.5x=y; since it is $2.52 PER gallon, you need to multiply the amount of gallons by the cost. In this case, it is 4.
2.5(4)=10
So, the price of 4 gallons is $10.