Question

The function A(b) relates the area of a trapezoid with a given height of 12 and

one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 12.579
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the othef base?

Answer 1

`B(a)=(a)/(6)-9`

Explanation:

see the attached figure , to better understand the problem

we have

`A(b)=12((b+9)/(2))`

where

A(b) ---> is the trapezoid's area

b ---> is the other base value

Solve the equation for b

That means ----> isolate the variable b

Divide 12 by 2 right side

`A=6(b+9)`

Divide by 6 both sides

`(A)/(6)=b+9`

subtract 9 both sides

`(A)/(6)-9=b`

Rewrite

`b=(A)/(6)-9`

Convert to function notation

`B(a)=(a)/(6)-9`