The area bounded by the x-axis, the curve $y=f\left(x\right),$ and the lines $x=1,x=b$ is equal to $\sqrt{b^2+1}-\sqrt{2}$ for all $b>1,$ then $f\left(x\right)$ is $\sqrt{x-1}$ (b) $\sqrt{x+1}$$\sqrt{x^2+1}$ (d) $\frac{x}{\sqrt{1+x^2}}$

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