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# Domain

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Let f(x) = x^2 + 2x + 5. If the domain of f is all real numbers, then f does not have an inverse function, but if we restrict the domain of f to an interval [c,\infty), then f may have an inverse function. What is the smallest value of c we can use here, so that f does have an inverse function?

Jun 23, 2021

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x^2 + 2x + 5 = (x+1)^2 + 3.

At x = c, the parabola becomes a reflection of itself.

Where is c?

=^._.^=

Jun 23, 2021