The inverse of f(x)=2x−1x+5 may be written in the form f−1(x)=ax+bcx+d, where a, b , c, and d are real numbers. Find a/c.
y = 2x-1/x+5 First, solve for 'x'
yx+5y -2x = -1
yx - 2x= -5y -1
x(y-2) = -5y-1
x = (-5y-1)/(y-2) then switch the x's and y's to have the inverse f^-1 (x)
y = (-5x-1)/(x-2) a = -5 c= 1 a/c -5/1 = -5
y = 2x-1/x+5 First, solve for 'x'
yx+5y -2x = -1
yx - 2x= -5y -1
x(y-2) = -5y-1
x = (-5y-1)/(y-2) then switch the x's and y's to have the inverse f^-1 (x)
y = (-5x-1)/(x-2) a = -5 c= 1 a/c -5/1 = -5