What is the range of (2x^2-10)/(x+2) ?

The range of (2x^2-10)/(x+2) is -infinity <f(x)<infinity

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range of (2x^2-10)/(x+2)

range

\frac{2 x ^{2} - 10}{x + 2}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{2 x ^{2} - 10}{x + 2} = y

Multiply both sides by

x + 2

2 x^{2} - 10 = y (x + 2)

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

Discriminant

2 x^{2} - 10 = y (x + 2) : y^{2} + 80 + 16 y

y^{2} + 80 + 16 y \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

What is the range of (2x^2-10)/(x+2) ?
The range of (2x^2-10)/(x+2) is -infinity <f(x)<infinity