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) = 14 * (b + 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? N(c) = (c + 15)/20; n(c) = (c + 20)/15; n(c) = (c - 20)/15; n(G) = (Q - 15)/20

Answer 1

Answer:

$b(a) = \frac{a}{7} -5$

Step-by-step explanation:

Given

$a(b) = 14 * \frac{b + 5}{2}$

Required

The inverse function

We have:

$a(b) = 14 * \frac{b + 5}{2}$

$a(b) = 7(b + 5)$

Rewrite as:

$a = 7(b + 5)$

Divide by 7

$\frac{a}{7} =b + 5$

Subtract 5

$b = \frac{a}{7} -5$

Express as:

$b(a) = \frac{a}{7} -5$ --- the inverse function