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Question: If \(f^{- 1}(x) = \frac{x + 4}{3}\) then \(\lbrack f\{ f(x)\}\rbrack\) equals...

If f−1(x)=x+43f^{- 1}(x) = \frac{x + 4}{3} then [f{f(x)}]\lbrack f\{ f(x)\}\rbrack equals

A

x

B

⇒\Rightarrow

C

x2\frac{x}{2}

D

−1x- \frac{1}{x}

Answer

x

Explanation

Solution

f[f(x)]=2(2x−3x−2)−3(2x−3x−2)−2=xf\lbrack f(x)\rbrack = \frac{2\left( \frac{2x - 3}{x - 2} \right) - 3}{\left( \frac{2x - 3}{x - 2} \right) - 2} = x