Question

if f:R-{3}is a relation defined by f(x)=x+3/x-3 then for x not equal to 1 ,f[3x+3/x-1]
the who answer first correctly is marked as brainliest

Answer 1

f :  R - {3} --> R.
f(x) =  (x+3) / (x-3)     , x≠3

x≠1,  
$f(\frac{3x+3}{x-1})=\frac{\frac{3x+3}{x-1}+3}{\frac{3x+3}{x-1}-3}\\\\=\frac{6x}{6}=x$

ans:  x

Since,  f( 3x+3 / x-1 ) = x,  we can say that  inverse of f,  ie., f^-1 (x) = 3x+3 / x-1 ,  
 
 f^-1 :   R - {1}  --> R