What is the f(x)=sqrt(x^2-x+1) ?

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f(x)=sqrt(x^2-x+1)

f (x) = x^{2} - x + 1

Domain : - \infty < x < \infty

Range : f (x) \geq \frac{3}{2}

Y Intercepts : (0, 1)

Asymptotes : Slant y = x - \frac{1}{2}, y = - x + \frac{1}{2}

Extreme Points : Minimum (\frac{1}{2}, \frac{3}{2})

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

x^{2} - x + 1 : - \infty < x < \infty

Range of

x^{2} - x + 1 : f (x) \geq \frac{3}{2}

Axis interception points of

x^{2} - x + 1 :

Y Intercepts

: (0, 1)

Asymptotes of

x^{2} - x + 1 :

Slant

: y = x - \frac{1}{2}, y = - x + \frac{1}{2}

Extreme Points of

x^{2} - x + 1 :

Minimum

(\frac{1}{2}, \frac{3}{2})

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