Question

The function A(b) relates the area of a trapezoid with a given height of 10 and

Answer 1

Answer:

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

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height $*$ ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 $*$ ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 $*$ ( ( y + 7 ) / 2 ) or $b=\frac{\left(y+7\right)\cdot \:10}{2}$ - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

$y+7=\frac{a}{5}$,

$y^{-1}=\frac{a}{5}-7 = B(a)$

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7