Let A - x - R -1 - x - 1- B and C - x - R - x - 0 andlet S - x - y - A - B - x 2- y 2-1 and S 0- x - y - A - C - x 2- y 2-1- Then-a S defines a function from A to Bb S0 defines a function from A to Cc S0 defines a function from A to Bd S defines a function from A to C

(a) S defines a function from A to B Let #160;x #8712;A #8658; 1 #8804;x #8804;1Now, #160;x2+y2=1 #8658;y2=1 x2 #8658;y= #177;1 x2 #8658; 1 ...

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Integration of Piecewise Continuous Functions

Let A = x ∈ R...

Question

Let $A = \{x \in R : - 1 \leq x \leq 1\} = B and C = \{x \in R : x \geq 0\} and$
let $S = \{(x, y) \in A \times B : x^{2} + y^{2} = 1\} and S_{0} = \{(x, y) \in A \times C : x^{2} + y^{2} = 1\}$ . Then,
(a) S defines a function from A to B
(b) S₀ defines a function from A to C
(c) S₀ defines a function from A to B
(d) S defines a function from A to C

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A = [- 1, 1], B = [- 1, 1], C = [0, \infty)

R_{1} = {(x, y) \in A \times B : x^{2} + y^{2} = 1}

R_{2} = {(x, y) \in A \times C : x^{2} + y^{2} = 1}

A = [- 1, 1], B = [- 1, 1], C = [0, \infty)

R_{1} = {(x, y) \in A \times B : x^{2} + y^{2} = 1}

R_{2} = {(x, y) \in A \times C : x^{2} + y^{2} = 1}

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{(x, y) ϵ A \times B : x^{2} + y^{2} = 1}

R_{2} = {(x, y) ϵ A \times C : x^{2} + y^{2} = 1}

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