Question

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

Answer 1

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]}