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

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

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range of (x-1)/((x-2)(x+4))

range

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

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

(x - 2) (x + 4)

x - 1 = y (x - 2) (x + 4)

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

Discriminant

x - 1 = y (x - 2) (x + 4) : 36 y^{2} - 8 y + 1

36 y^{2} - 8 y + 1 \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = \frac{- 2}{x - 2}

f (x) = \frac{x - 6}{6}

f (x) = - 4 x - 5

5^{x} + 3

x - 2

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