f(x) = 5x+3/4x-5 , show that f(f(x)) is an identity function . hence find f inverse of x

Consider the following function.    fx=5x+34x-5It is required to show that ffx is an identity function.To find  ffx replace x with5x+34x-5 in  fx   ffx=55x+34x-5+345x+34x-5-5            =55x+3+34x-545x+3-54x-5    take LCM in numerator and denominator            =25x+15+12x-1520x+12-20x+25            =37x37            =x            =Ix ,   where I is an identity functionThus it is proved that  ffx is an identity functionNow we know that if    fg=gf=IThen g is inverse of fHere  ffx=f°f x=I, so the inverse of the function f is "f" itself.       

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