If the function $f : R \to R$ is defined by $f(x) = log_a(x + \sqrt {x^2 +1} ), (a > 0, a \neq 1)$, then $f^{-1}(x)$ is
If the function $f : R \to R$ is defined by $f(x) = log_a(x + \sqrt {x^2 +1} ), (a > 0, a \neq 1)$, then $f^{-1}(x)$ is
- A
$\left( {\frac{{{a^x} + {a^{ - x}}}}{2}} \right)$
- B
$\left( {\frac{{{a^x} - {a^{ - x}}}}{2}} \right)$
- C
Doesn't exist $\forall x \in R$
- D
Exists for $x \in R^+$ only
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