Find the domain , range and inverse of f(x) = ax+b / cx+d where a , b , c , d ∈ R and ad-bc =1

Question

Find the domain , range and inverse of f(x) = ax+b / cx+d where   a  ,  b  ,  c  ,  d  ∈      R   and ad-bc =1

juicilysv · Accepted Answer

Find the domain , range and inverseof f(x) = ax+b / cx+d where a,b,c,d and ad-bc =1domain is R-{cx+d=0} that is    R  −      {                  −        d            c        }  For inverse of   y  =  f  (  x  )  =            a      x      +      b              c      x      +      d        ⇒  y  c  x  +  y  d  =  a  x  +  b  ⇒  c  y  x  −  a  x  =  −  d  y  +  b  ⇒  x  (  c  y  −  a  )  =  −  d  y  +  b  (  c  y  −  a  )  =  −  d  y  +  b  x  =            −      d      y      +      b              c      y      −      a        ⇒  x  =            −      d      y      +      b              c      y      −      a        ⇒      f          −      1        (  x  )  =            −      d      x      +      b              c      x      −      a

Paxton Hoffman · Accepted Answer

The inverse of the finction is   y  =            d      x      −      b              a      −      c      x      . To find this, u replace all of the x&#039;s with y&#039;s and all of the y&#039;s with x&#039;s. then u solve for y.I think that the domain is all real numbers except -d/c and the range is all of the real numbers except f(-d/c)

Find the domain , range and inverse of f(x) = ax+b / cx+d where a,b,c,d in mathbb(R) and ad-bc =1

Answered question

Answer & Explanation

New Questions in Differential Calculus