inverse function.

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$\hspace{-16}$If $\mathbf{f:\mathbb{R}\rightarrow \mathbb{R}}$ and $\mathbf{f(x)=\ln(x+\sqrt{x^2+1})}$\\\\ Then no. of solution of the equation $\mathbf{\mid f^{-1}(x)\mid = e^{-\mid x \mid}}$ is$

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rishabh ·Mar 12 '12 at 4:53

we can find the inverse by the usual method which comes out to be,
e^x-e^-x2

so drawing both the graphs we get 2 points

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Aditya Bhutra ·Mar 12 '12 at 6:53

yes , f^-1(x) = e^x - e^-x2

for x>0 , e^x - e^-x =2e^-x , e^x=âˆš3 ...(1 soln)

for x<0 , e^x - e^-x = 2e^x , e^2x = -1/2 (no soln)

so total only 1 soln.

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Basic Integral Calculus Operators Symbols Matrix Cases

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° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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inverse function.

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