What is the range of (x^2+2x-1)/(x+1) ?

The range of (x^2+2x-1)/(x+1) is -infinity <f(x)<infinity

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

range

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

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x ^{2} + 2 x - 1}{x + 1} = y

Multiply both sides by

x + 1

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

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

Discriminant

x^{2} + 2 x - 1 = y (x + 1) : y^{2} + 8

y^{2} + 8 \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

\frac{2 t ^{2} - 5}{3 t + 6}

f (x) = 2 x^{3} - 6 x^{2} - 18 x + 5

f (x) = x - 2 + 7

4 - x^{2}

f (x) = x^{\frac{1}{3}} (x + 4)

What is the range of (x^2+2x-1)/(x+1) ?
The range of (x^2+2x-1)/(x+1) is -infinity <f(x)<infinity