What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?

Explanation

Complete the square for the quadratic expression: x^2 + 2x + 11 = (x+1)^2 + 10. The minimum value of (x+1)^2 is 0, which occurs at x = -1. Therefore, the minimum value of the expression inside the logarithm is 10. The minimum value of the function is f(-1) = \log_{10}(10) = 1.

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