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 Transitive Relation. Give one example.

Let A be the set of all human beings in a town at a particular time. Determine whether the relation R = {(x, y) : x is wife of y ; x, Y\(\in \)A} is reflexive, symmetric and transitive.

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

Let a*b = 2a + b - 3, find 3*4.

Consider \(f:R_{ + }\rightarrow [-5,\infty )\) given by f(x) = 9x² + 6x - 5 Show that f is invertible find f^-1(x) where R₊ is the set of all non-negative real numbers.

Let A = \(R\times R\) and * be a binary operation on A defined by 
(a,b)*(c,d) = (a+c, b+c)
Show that * is commutative and associative. Find the identity element for * on A. Also find • the inverse of every element (a, b)  \(\in A\) *.