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F (x) = LG [x + √ (x ^ 2 + 1)] to find the inverse function of F (x) Each step is more detailed The answer is y = 1 / 2 (10 ^ X-10 ^ - x)
Y = LG [x + √ (x ^ 2 + 1)], the definition field is r, and the value field is r
x+ √(x^2+1) =10^y=A>0
(x^2+1)=(A-x)^2
1=A^2-2Ax
x=(A^2-1)/(2A)=(100^y-1)/(2*10^y)
So the inverse function is y = (100 ^ x-1) / (2 * 10 ^ x), and X is r
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