f:x→x+2x−3,x≠3,f=?f : x \rightarrow \frac{x+2}{x-3}, x \neq 3, f = ?f:x→x−3x+2,x=3,f=?
Let f:x=yf : x=yf:x=y
y=x+2x−3y=\frac{x+2}{x-3}y=x−3x+2
=x+2=y(x−3)=x+2=y(x-3)=x+2=y(x−3)
=x−xy=−3y−2=x-xy=-3y-2=x−xy=−3y−2
=x(1−y)=−3y−2=x(1-y)=-3y-2=x(1−y)=−3y−2
=x=−3y−21−y=−(3y+2)−(y−1)=x=\frac{-3y-2}{1-y}=\frac{-(3y+2)}{-(y-1)}=x=1−y−3y−2=−(y−1)−(3y+2)
=x=3y+2y−1=x=\frac{3y+2}{y-1}=x=y−13y+2
∴f−1:x=3x+2x−1,x≠1\therefore f^{-1} : x=\frac{3x+2}{x-1}, x \neq 1∴f−1:x=x−13x+2,x=1