range of (x^2+x+1)/x

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for expand factor rationalize

See All

area

asymptotes

critical points

derivative

domain

eigenvalues

eigenvectors

expand

extreme points

factor

implicit derivative

inflection points

intercepts

inverse

laplace

inverse laplace

partial fractions

range

slope

simplify

solve for

tangent

taylor

vertex

geometric test

alternating test

telescoping test

pseries test

root test

Steps Examples

Generated by AI

range x²+x+1x

Solution

f(x)≤ −1 or f(x)≥ 3

Interval Notation

(−∞ , −1]∪ [3, ∞ )

Show Steps

Hide Steps

Solution steps

One step at a time

Function range definition

The set of values of the dependent variable for which a function is defined

Rewrite as

x²+x+1x =y

Multiply both sides by x

x²+x+1=yx

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant x²+x+1=yx: y²−2y−3

y²−2y−3≥ 0 : y≤ −1 or y≥ 3

Check if the range interval endpoints are included

y=−1 : Included

y=3 : Included

Therefore the range is

f(x)≤ −1 or f(x)≥ 3

Solve instead

domain x²+x+1x

inverse x²+x+1x

intercepts x²+x+1x

Dice Problems Examples

Popular topics

median calculator dot product calculator arc length calculator maclaurin series calculator z score calculator critical point calculator inequalities calculator range calculator determinant calculator second derivative calculator lcm calculator partial derivative calculator complete the square calculator distributive property calculator mixed fractions calculator Time Calculator gradient calculator triple integrals calculator partial fractions calculator indefinite integral calculator solve for x calculator double integral solver vector calculator Date Calculator vertex calculator binomial expansion calculator decimal to fraction calculator difference quotient calculator eigenvalue calculator piecewise functions calculator radius of convergence calculator roots calculator exponential function calculator interval of convergence calculator fractions divide calculator inflection point calculator expand calculator variance calculator fractions multiply calculator fourier series calculator foil calculator modulo calculator series convergence calculator linear algebra calculator

−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

range of (x^2+x+1)/x

Solution

Solution steps

Solve instead

Number Line

Graph