Find the range of the function gx x2 2 if xSolutionx2 is alw

Find the range of the function g(x). x2 +2 if x

Solution

x^2 is always greater or equal to 0

min value occurs 0 at x=0 which clearly falls in given restriction x<3

so min value for x^2+2=0+2=2

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x-5 is increasing function so min value will occurat at x=3

which is 3-5=-2

lowest of -2 and 2 is -2

so the range will be [-2,infinity)

Hence 2nd choice is correct.