Question

The function f is one to one. Find its inverse. State the domain of f and find its range using f^-1

f(x)= -9x/x-1

f^-1(x)=_______
domain f=______
range f=_______

Answer 1

x-1=0
x = 1
plug x = 1 find y
-9(1)/1-0 =0 \[x(y-1)=-9y\]
y =0\[y=\frac{-9x}{x-1}\]Substitution x=y\[x=\frac{-9y}{y-1}\]\[x(y-1)=-9y\]
\[xy-x=-9y\]\[xy+9y=x\]\[y(x+9)=x\]\[y=\frac{x}{x+9}\]
\[f^-1=\frac{x}{x+9}\]domain f=1
range f=0