Is the following relation a function ? Justify your answer:
(i) `R_(1) = {(2,3), ((1)/(2), 0), (2,7), (-4,6)}`
(ii) `R_(2) = {(x,|x|): x" is a real number" )`

Do the following equations represent a pair of coincidnet lines? Justify your answer. -2x-3y=1, 6y+ 4x= -2

Solve the equation and verify your answer: (7x-2)/(5x-1)=(3x-4)/(x+6)

Do the following pair of linear equations have no solution ? Justify your answer. (i) 2x + 4y = 3 and 12y +6x = 6 (ii) x = 2y and y = 2x (iii) 3x + y - 3 = 0 and 2x + (2)/(3)y = 2

Find R^(-1) , when (i) R={(1,2),(1,3),(2,3),(3,2),(4,5)}, (ii) R={(x,y):x,yinN,x+2y=8}.

Do the following equations represent a pair of coincident lines ? Justify your answer. (i) 3x + (1)/(7)y = 3 and 7x + 3y = 7 (ii) -2x - 3y = 1 and 6y + 4x = -2 (iii) (x)/(2) + y + (2)/(5) = 0 and 4x + 8y + (5)/(16) = 0

which of the following expressions are polynomials ? Justify your answere, (i) 8 (ii) sqrt(3x)^(2)-2x (iii) 1-sqrt(5x) (iv) (1)/(5x^(-2))+5x+7 (v) ((x-2)(x-4))/(x) (vi) (1)/(x+1) (vii) (1)/(7)a^(3)-(2)/(sqrt(3))a^(2)+4a-7 (viii) (1)/(2x)

Are the following pair of linear equations consistent ? Justify your answer. (i) -3x - 4y = 12 and 4y + 3x = 12 (ii) (3)/(5)x - y = (1)/(2) and (1)/(5) x - 3y = (1)/(6) (iii) 2ax + by = a and 4ax + 2by - 2a = 0, a, b != 0 (iv) x + 3y = 11 and 2(2x + 6y) = 22

Determine the domain and range of the relation R defined by : (i) R= {(x+1, x+5), x in {0,1,2,3,4,5}} (ii) R= { (x, x^(3)): x is prime number less than10}

Find the range of each of the following functions. (i) f(x)" "=" "2" "" "3x ," "x in R , x" ">" "0 (ii) f(x)" "=x^2+" "2 , x is a real number. (iii) f(x)" "=" "x , x is a real number.