If , show that f o f ( x ) = x , for all . What is the inverse of f ?

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Solution

The given function is f( x )= ( 4x+3 ) ( 6x−4 )

The equation to calculate inverse of the function f( x ) is,

( fof )( x )=f( f( x ) ) =f( 4x+3 6x−4 ) = 4( 4x+3 6x−4 )+3 6( 4x+3 6x−4 )−4 = 16x+12+18x−12 24x+18−24x+16 = 34x 34 =x

Therefore, ( fof )( x )=x , for all x≠ 2 3 . So fof=1 .

Thus, the function f is invertible and the inverse of f is f itself.

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

x \neq \frac{2}{3}

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

If, show that f o f(x) = x, for all. What is the inverse of f?

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

x \neq \frac{2}{3}

f o f (x) = x

x \neq \frac{2}{3}

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

f o f (x) = x

x \neq \frac{2}{3}

f

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