Question

The function A(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 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)=14xb+5/2 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 other base? A. B(a)+a/7+5 B. B(a)=a/5-7 C. B(a)=a/7-5 D. B(a)=a/5+7

Answer 1

`b(a) =(a)/(7) -5`

Explanation:

Given

`A(b) = 14 * (b + 5)/(2)`

Required

Determine the inverse function b(a)

Write A(b) as a

`a = 14 * (b + 5)/(2)`

Swap a and b

`b = 14 * (a + 5)/(2)`

`b = 7(a + 5)`

Divide both sides by 7

`a + 5 = (b)/(7)`

Maka a the subject

`a =(b)/(7) -5`

Swap a and b again

`b =(a)/(7) -5`

Hence:

`b(a) =(a)/(7) -5`