Solve `3x+8 gt2`, when
(i) x is an integer.
(ii) x is a real number.

Solve 5x-3 lt 7 , when (i) x is an integer. (ii) x is a real number.

Solve -12x gt 30 , when (i) x is a natural number. (ii) x is an integer.

Solve 24x lt 100 , when (i) x is a natural number, (ii) x is an integer.

a gt 1 is a real number f(x) = log_(a)x^2 , where x gt 0 If f^(-1)(x) is a inverse of f(x) and b and c are real numbers then f^(-1) (b+c) = ......

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

Let {x} and [x] denotes the fraction fractional and integral part of a real number (x) , respectively. Solve |2x-1|=3[x]+2{x} .

Find the zero of the polynomial in each of the following cases. (i) f (x) = x +2 (ii) f (x) = x-2 (iii) f (x) =2x +3 (iv) f (x) =2x -3 (v) f (x) =x ^(2) (vi) f (x) = px, p ne 0 (vii) f (x) = px + q,p ne 0 pq are real numbers.

Match roster forms with the set builder form. (i) {p,r,I,n,c,a,l} (a) {x : x is a positive integer and is a divisor of 18} (ii) {0} (b) {x : x is an integer and x^(2)-9=0} (iii) {1,2,3,6,9,18} (c) {x : x is an integer and x+1=1} (iv) {3,-3} (d) {x : x is a letter of the word PRINCIPAL}

Check whether the following pair of statements are negation of each other. Give reasons for your answer: (i) x+y=y+x is true for every real numbers x and y. (ii) There exists real number x and y for which x+y=y+x