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

1 Answer
Feb 10, 2016

Answer:

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

Explanation:

#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]}