Domain-of-the-explicit-form-of-the-function-y-represented-implicitly-by-the-equation-1-x-cosy-x-2-0-is-a-1-1-b-1-1-5-2-c-1-5-2-1-5-2-d-0-

Question Number 39464 by nishant last updated on 06/Jul/18

D o m a i n o f t h e e x p l i c i t f o r m o f

t h e f u n c t i o n y r e p r e s e n t e d

i m p l i c i t l y b y t h e e q u a t i o n

(1 + x) c o s y - x^{2} = 0 i s

(a) (- 1, 1] (b) (- 1, 1 - \sqrt{} 5 / 2]

(c) [1 - \sqrt{} 5 / 2, 1 + \sqrt{} 5 / 2]

(d) [0, 1 + \sqrt{} 5 / 2]

Answered by MJS last updated on 06/Jul/18

\cos y = \frac{x^{2}}{x + 1} \Rightarrow x \neq - 1 \land \frac{x^{2}}{∣ x + 1 ∣} ⩽ 1

x^{2} ⩽∣ x + 1 ∣

f (x) = x^{2} - x - 1 = 0 \Rightarrow x_{1} = \frac{1}{2} - \frac{\sqrt{5}}{2}; x_{2} = \frac{1}{2} + \frac{\sqrt{5}}{2}

f (x) = x^{2} + x + 1 = 0 \Rightarrow no real solution

(\frac{1}{2} - \frac{\sqrt{5}}{2} ⩽ x ⩽ \frac{1}{2} + \frac{\sqrt{5}}{2})

domain is [\frac{1}{2} - \frac{\sqrt{5}}{2}; \frac{1}{2} + \frac{\sqrt{5}}{2}]

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