What is the range of f(x)= 6/(x^2-16) ?

The range of f(x)= 6/(x^2-16) is f(x) 0

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range of f(x)= 6/(x^2-16)

range

f (x) = \frac{6}{x ^{2} - 16}

f (x) \leq - \frac{3}{8} or f (x) > 0

Interval Notation

(- \infty, - \frac{3}{8}] \cup (0, \infty)

Solution steps

Rewrite as

\frac{6}{x ^{2} - 16} = y

Multiply both sides by

x^{2} - 16

6 = y (x^{2} - 16)

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

Discriminant

6 = y (x^{2} - 16) : 64 y^{2} + 24 y

64 y^{2} + 24 y \geq 0 : y \leq - \frac{3}{8} or y \geq 0

Check if the range interval endpoints are included

y = - \frac{3}{8} :

Included

y = 0 :

Excluded

Therefore the range is

f (x) \leq - \frac{3}{8} or f (x) > 0

y = - 3 x + 4

- 4

f (x) = x^{4} - 8 x^{2} + 16

2^{- x} + 4

(2, - 3), (8, - 9)

What is the range of f(x)= 6/(x^2-16) ?
The range of f(x)= 6/(x^2-16) is f(x)<=-3/8 \lor f(x)>0