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What is the domain and range of #g(x)=2x^2-x+1#?

Answer 1

Domain: #RR#
Range: #RR >=7/8#

#g(x)=2x^2-x+1# is defined for all Real values of #x# So Domain #g(x) = RR#

#g(x)# is a parabola (opening upward) and we can determine its minimum value by re-writing its expression in vertex form:

#2x^2-x+1# #=2(x^2-1/2xcolor(blue)(+(1/4)^2))+1 color(blue)(-1/8)# #=2(x-1/4)^2+7/8# #color(white)("XXXXXXXXX")#with vertex at #(1/4,7/8)#

So the Range #g(x) = RR >=7/8# graph{2x^2-x+1 [-2.237, 3.24, -0.268, 2.47]}

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Answer 2

Nathan Axel

Domain: All real numbers Range: All real numbers greater than or equal to 1/2

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.