What is the range of (3x+4)/(x^2-25) ?

The range of (3x+4)/(x^2-25) is -infinity <f(x)<infinity

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range of (3x+4)/(x^2-25)

range

\frac{3 x + 4}{x ^{2} - 25}

- \infty < f (x) < \infty

Solution steps

Rewrite as

\frac{3 x + 4}{x ^{2} - 25} = y

Multiply both sides by

x^{2} - 25

3 x + 4 = y (x^{2} - 25)

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

Discriminant

3 x + 4 = y (x^{2} - 25) : 9 + 100 y^{2} + 16 y

9 + 100 y^{2} + 16 y \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

y = 5 x + 2, at x = 1

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

f (x) = \frac{x - 5}{x ^{2} - 25}

f (x) = \frac{1 - 2 t}{( t + 6 )}

- x^{4} + 12 x^{3} - 12 x + 13

What is the range of (3x+4)/(x^2-25) ?
The range of (3x+4)/(x^2-25) is -infinity <f(x)<infinity