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

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

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range of f(x)=ln(x^2)

range

f (x) = 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) = x^{2} + 12

- \frac{3}{2} x + \frac{3}{2}

f (x) = 4 x - 8

f (x) = 7 x - 2

f (x) = e^{x - 3}

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