a-3-1-5-the-set-of-possible-values-of-a-a-b-3-e-a-3-

Question Number 127305 by MathSh last updated on 28/Dec/20

{(a - 3)}^{- \frac{1}{5}}

t h e s e t o f p o s s i b l e v a l u e s o f a

a) (- \infty; + \infty)

b) (3; + \infty)

e) a \neq 3

Answered by MJS_new last updated on 28/Dec/20

depending on the definition we use \dots

b = \frac{1}{\sqrt[5]{a - 3}}

(1) a \in R \land b \in R; \sqrt[5]{x} = sign x \sqrt[5]{∣ x ∣} (i . e . \sqrt[5]{- 32} = - 2

\Rightarrow a \neq 3 \Rightarrow a \in R ∖ {3}

(2) a \in C \land b \in C; \sqrt[5]{x} =∣ x ∣ e^{i \frac{\arg x}{5}}

\Rightarrow a \neq 3 \Rightarrow a \in C ∖ {3}

Commented by MathSh last updated on 28/Dec/20

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