write an equation of the inverse for the one - to - one function as defined. \n(a(x)=-2x + 9) \nthe equation…

Explanation:

Step1: Replace ( a(x) ) with ( y )

We start by writing the function as ( y = -2x + 9 ). This is a standard step to make it easier to swap the variables ( x ) and ( y ) when finding the inverse.

Step2: Swap ( x ) and ( y )

After swapping, we get ( x = -2y + 9 ). This step is based on the definition of an inverse function, where the input and output of the original function are reversed in the inverse function.

Step3: Solve for ( y )

First, subtract 9 from both sides: ( x - 9 = -2y ). Then, divide both sides by -2: ( y=\frac{9 - x}{2}) or ( y = -\frac{x}{2}+\frac{9}{2}). This gives us the equation of the inverse function.

Answer:

( -\frac{x}{2}+\frac{9}{2} ) (or equivalently ( \frac{9 - x}{2} ))