What is the range of f(x)=(x^2-4)/(x+1) ?

The range of f(x)=(x^2-4)/(x+1) is -infinity <f(x)<infinity

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range of f(x)=(x^2-4)/(x+1)

range

f (x) = \frac{x ^{2} - 4}{x + 1}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x ^{2} - 4}{x + 1} = y

Multiply both sides by

x + 1

x^{2} - 4 = y (x + 1)

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

Discriminant

x^{2} - 4 = y (x + 1) : y^{2} + 16 + 4 y

y^{2} + 16 + 4 y \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

What is the range of f(x)=(x^2-4)/(x+1) ?
The range of f(x)=(x^2-4)/(x+1) is -infinity <f(x)<infinity