Let f:[1, ∞) arrow[3, ∞) be defined as f(x)=( log 2 x)2+2( log 2 x)+3. If f-1 is the inverse function of f, then f-1(x) is equal to

Question

Let f:[1, ∞) arrow[3, ∞) be defined as f(x)=( log 2 x)2+2( log 2 x)+3. If f-1 is the inverse function of f, then f-1(x) is equal to (A) 2-1-√x-2 (B) 2√x-3 (C) 22 √x-3 (D) 2-1+√x-2

Tardigrade Admin · Accepted Answer

f(x)=(( log 2 x)+1)2+2 ⇒ f -1( x )=2-1+√x-2

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

$2^{- 1 - x - 2}$

$2^{x - 3}$

$2^{2 x - 3}$

$2^{- 1 + x - 2}$

$f (x) = ((lo g_{2} x) + 1)^{2} + 2$
$\Rightarrow f^{- 1} (x) = 2^{- 1 + x - 2}$

Q. Let f:[1,∞)→[3,∞) be defined as f(x)=(log2​x)2+2(log2​x)+3. If f−1 is the inverse function of f, then f−1(x) is equal to

2−1−x−2​

2x−3​

22x−3​

2−1+x−2​