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Popular Functions >

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

Solution

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

Solution

Domain : - \infty < x < \infty

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

Y Intercepts : (0, 1)

Asymptotes : Horizontal y = 1

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{2}, \frac{3}{2}]

Solution steps

Domain of

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

Range of

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

Axis interception points of

\frac{x ^{2} - x + 1}{x ^{2} + 1} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{x ^{2} - x + 1}{x ^{2} + 1} :

Horizontal

: y = 1

Extreme Points of

\frac{x ^{2} - x + 1}{x ^{2} + 1} :

Maximum

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

Minimum

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

Graph

Popular Examples

f(x)=2cos(3x+pi)-1

f(x)=2(x)^2+5sqrt((x+2))

f(x)=(2(x+2)^2)/(x^2)

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

f(x)=(3sqrt(x^2-9))/(x-1)

Frequently Asked Questions (FAQ)

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