What is the range of y=ln(x^2-4) ?

The range of y=ln(x^2-4) is -infinity <f(x)<infinity

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range of y=ln(x^2-4)

range

y = ln (x^{2} - 4)

- \infty < f (x) < \infty

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

ln (x^{2} - 4)

Inverse of

ln (x^{2} - 4) : e^{x} + 4, - e^{x} + 4

e^{x} + 4, - e^{x} + 4

Find the domain of each inverse function

Domain of

e^{x} + 4 : - \infty < x < \infty

Domain of

- e^{x} + 4 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

(- 8, 3), (- 5, - 2)

f (x) = 2^{x} - 1

f (x) = \frac{1}{5} x + \frac{4}{15}

(- 2.1) (3.9)

3 x - 2 y = - 10

What is the range of y=ln(x^2-4) ?
The range of y=ln(x^2-4) is -infinity <f(x)<infinity