What is the range of-ln(x^2-1) ?

The range of-ln(x^2-1) is -infinity <f(x)<infinity

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range of-ln(x^2-1)

range

- ln (x^{2} - 1)

- \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} - 1)

Inverse of

- ln (x^{2} - 1) : e^{- x} + 1, - e^{- x} + 1

e^{- x} + 1, - e^{- x} + 1

Find the domain of each inverse function

Domain of

e^{- x} + 1 : - \infty < x < \infty

Domain of

- e^{- x} + 1 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

f (x) = 5 - 7 x

(6.16) (2.4)

f (x) = lo g_{6} (3^{x})

y = \frac{1}{2} x - 1, (6, 2)

What is the range of-ln(x^2-1) ?
The range of-ln(x^2-1) is -infinity <f(x)<infinity