F(c) = 1/x+5 -1 find the inverse function of f(x) and it’s domain

f ( x ) = 1/x+5 - 1

y = 1/x+5 - 1

Add both sides 1

y + 1 = 1/x+5 - 1 + 1

y + 1 = 1/x+5

Multiply both sides by ( x + 5 )

( x + 5 ) × ( y + 1 ) = ( x + 5 ) × 1 / x + 5

xy + x + 5y + 5 = 1

x( y + 1 ) + 5y + 5 = 1

Subtract both sides 5

x( y + 1 ) + 5y + 5 - 5 = 1 - 5

x( y + 1 ) + 5y = - 4

Subtract both sides 5y

x( y + 1 ) + 5y - 5y = - 4 - 5y

x( y + 1 ) = - 5y - 4

Divide both sides by ( y + 1 )

x( y + 1 ) ÷ ( y + 1 ) = ( - 5y - 4 ) ÷ ( y + 1 )

x = - 5y - 4 / y + 1

Thus the inverse function of f(x) is :

y = - 5x - 4 / x + 1 ( D : R - { - 1 } )

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

add a pic of the graph, then ill edit this "answer" and solve it for you : 3

step-by-step explanation: