Question- 1 - xa-b1 -a-c-1 - xb-c1 -b-a-1 - xc-a1 -c-b-A 0BC a-b-cD a-b-c2

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Continuity of Composite Functions

Question:- 1 ...

Question

Question:- (1/x^a-b)^1/(a-c) . (1/x^b-c)^1/(b-a) . (1/x^c-a)^1/(c-b) = ?

A) 0

B) 1

C) (a+b+c)

D) (a-b+c)²

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{(\frac{1}{x^{a - b}})}^{\frac{1}{(a - c)}} . {(\frac{1}{x^{b - c}})}^{\frac{1}{(b - a)}} . {(\frac{1}{x^{c - a}})}^{\frac{1}{(c - b)}} =

\frac{1}{1 + x^{(b - a)} + x^{(c - a)}} + \frac{1}{1 + x^{(a - b)} + x^{(c - b)}} + \frac{1}{1 + x^{(b - c)} + x^{(a - c)}} = ?

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{a - c} + x^{b - c}}

Prove that:

(i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

(ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1

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