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

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

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range of ln(x^2)

range

ln (x^{2})

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

ln (x^{2})

Inverse of

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

e^{x}, - e^{x}

Find the domain of each inverse function

Domain of

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

Domain of

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

Combine the intervals

- \infty < f (x) < \infty

f (x) = \frac{( 2 x ^{2} - 3 x - 20 )}{x - 5}

(1, - 3), (3, - 1)

f (x) = \frac{1}{7} (x^{3} - 1)

\frac{x + 6}{x - 2}

36 - x^{2}