What is the range of log_{10}(x^2-4) ?

The range of log_{10}(x^2-4) is -infinity <f(x)<infinity

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range of log_{10}(x^2-4)

range

lo g_{10} (x^{2} - 4)

- \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:

lo g_{10} (x^{2} - 4)

Inverse of

lo g_{10} (x^{2} - 4) : 1 0^{x} + 4, - 1 0^{x} + 4

1 0^{x} + 4, - 1 0^{x} + 4

Find the domain of each inverse function

Domain of

1 0^{x} + 4 : - \infty < x < \infty

Domain of

- 1 0^{x} + 4 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

f (x) = \frac{c}{x}

f (x) = \frac{4 x ^{2} - 5}{2 x ^{3} + x}

f (x) = - 7 x + 7

sin (3 x)

f (x) = 5 x^{2} - 4

What is the range of log_{10}(x^2-4) ?
The range of log_{10}(x^2-4) is -infinity <f(x)<infinity