If f(x) = x + 7 and g(x) = x - 7, \(X\in R,\) find fog(7)?

If the binary operation * on the set of integers Z is defined by a*b=a+3b² then find the value of 2 * 4.

Let * be a binary operation on N given by a*b=HCF(a,b), \(a,b\in N\). Write the value of 22*4.

If the binary operation * defined on Q is defined as a*b=2a+b-ab, for all \(a,b\in Q,\) find the value of 3*4.

If f:\(R\to R\) be defined by \(f(X)=(3-X^3)^{1\over3}\) then find fof(X).

Define Reflexive. Give one example.

Define symmetric Relation. Give one example

Define Transitive Relation. Give one example.

Let f:\(X\rightarrow Y\) be a function Define a relation R on X given be R=[(a,b) ; (f(b)] Show that R is an equivalence relation ?

Given an example of a relation which is
(i) Reflexive, Symmetric and transitive
(ii) Reflexive, Symmetric and not transitive.

If a*b = 3a + 4b, then value 3*4 is...........

If a*b \(=\frac { a }{ 2 } +\frac { b }{ 3 } \)then value of 2*3 is.......

Minimize Z = 3x + 2y subject to the constraints:
\(x+y\ge 8,3x+5y\le 15,x\ge 0,y\ge 0.\)

(Diet Problem) A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 unit/ kg of vitamin A and 1 unit/kg of vitamin C while food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs.50 per kg to purchase Food I and Rs.70 per kg to purchase food II.
Formulate the problem as a linear programming problem to minimise the cost of such a mixture.

Let * be a binary operation on Q defined by a*b = \(3ab\over5\). Show that * is commutative as well as associative. Also find its identify if it exists.

Show that the binary operation * on A = R-{-1} defined as a*b = a + b for all a, b, c A is  commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible