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

Answer:

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

Step-by-step explanation:

Given

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

Required

Determine the inverse function b(a)

Write A(b) as a

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

Swap a and b

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

$b = 7(a + 5)$

Divide both sides by 7

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

Maka a the subject

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

Swap a and b again

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

Hence:

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