Question

The function a(b) relates the area of a trapezoid with a given height of 10 and one base length of 7 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) = 10. b+7 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? O A. b(a) = 2 + 7 5 B. b(a)= O c. b(a) = a) = 2+5 D. b(a)= 7 1. 47​

Answer 1

The function for the trapezoid area is:

A(x)=(B+b)*h/2

where B and b are the bases and h is the height.

With the given data: h=10 B and b =7 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(7+x)*10/2

A(x)=(7+x)*5

So if you want the inverse function, you have to operate to find x:

A(x)/5=7+x

A(x)/5-7=x

So the new function is:

x(A)=A/5-7