What is the f(x)=(x^2+x+1)^{1/2} ?

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

f (x) = (x^{2} + x + 1)^{\frac{1}{2}}

Domain : - \infty < x < \infty

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

Y Intercepts : (0, 1)

Asymptotes : None

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

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

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

Range of

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

Axis interception points of

(x^{2} + x + 1)^{\frac{1}{2}} :

Y Intercepts

: (0, 1)

Asymptotes of

(x^{2} + x + 1)^{\frac{1}{2}} :

None

Extreme Points of

(x^{2} + x + 1)^{\frac{1}{2}} :

Minimum

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

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\frac{2 x}{3}