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if f(x)= 4x + 3 over 6x -4, x is not equal to 2 over 3, show that fof (x)=x, for all x not equal to 2 over 3. What is the inverse of f?

Q.4  If f(x) = \frac{4x + 3}{6x - 4}, x \neq \frac{2}{3} show that fof (x) = x,  for all x \neq\frac{2}{3}. What is the inverse of f?

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f(x) = \frac{4x + 3}{6x - 4}, x \neq \frac{2}{3}

fof (x) = x

(fof) (x) = f(f(x))

                    =f( \frac{4x + 3}{6x - 4})

                  =\frac{4( \frac{4x + 3}{6x - 4}) +3}{6( \frac{4x + 3}{6x - 4}) -4}

                = \frac{16x+12+18x-12}{24x+1824x+16}

                 = \frac{34x}{34}

                 \therefore fof(x) = x                ,  for all  x \neq \frac{2}{3}

\Rightarrow fof=Ix

Hence,the given function fis invertible and the inverse of f is f itself.

 

 

 

 

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