Question

Let $f:[1, \infty) \rightarrow[3, \infty)$ be defined as $f(x)=\left(\log _2 x\right)^2+2\left(\log _2 x\right)+3$. If $f^{-1}$ is the inverse function of $f$, then $f^{-1}(x)$ is equal to

• A. $2^{-1-\sqrt{x-2}}$
• B. $2^{\sqrt{x-3}}$
• C. $2^{2 \sqrt{x-3}}$
• D. $2^{-1+\sqrt{x-2}}$

Answer 1

Answer: (D)

$f(x)=\left(\left(\log _2 x\right)+1\right)^2+2$
$\Rightarrow f ^{-1}( x )=2^{-1+\sqrt{x-2}}$