X(8+y)=3y
Y=f^1(x)=(3x)/8x
8x=3yxy
8x=y(3x)
8x=y(x3)
X=3y/8+y
Y=f^1(x)=8x/3x
8x+xy=3y
1 Answer

You MUST use parentheses around denominator 8+x, or ANY denominator that consist of more than a single number of variable.
Also, don’t use lower case and upper case interchangeably.
In algebra, x and X are different, as are y and Y.
f(x) = y = 3x/(8+x)
Switch x and y, solve for y:
x = 3y/(8+y)
x(8+y) = 3y
8x+xy = 3y
8x = 3y−xy
8x = y(3−x)
y = f⁻¹(x) = 8x/(3−x)