Find The Domain Of f (x) = Log10 (1 + x3)

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Question

Find the domain of f (x) = log₁₀ (1 + x³)

easy

Solution

Correct option is

f (x) ,] –1, ∞[

f (x) = log10 (1 + x3) exists

if 1 + x3 > 0

⇒ (1 + x) (1 – x + x2) > 0;

{where (1 – x + x2) is always positive as D < 0 and a > 0.}

So, 1 + x > 0

or x > -1

or x ] –1, ∞[

Thus, domain of above function f (x) ,] –1, ∞[.

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