Relations and F...

For the pair of functions,
$$f\left( x \right) =9x-4,   g\left( x \right) =7x-9$$
Find $$\left( f-g \right) \left( x \right) $$.

Let a relation $$R$$ be defined by $$R=\left \{(4,5), (1,4), (4,6), (7,6), (3,7)\right \}$$. The relation $$R^{-1}\circ R$$ is given by

If $$A=\left \{1, 2,3\right \}$$ and $$B=\left \{3,8\right \}$$, then $$(A\cup B)\times (A\cap B)$$ is equal to

The relation $$R$$ defined on the set $$A=\left \{1,2,3,4,5\right \}$$ by $$R=\left \{(x,y):|x^2-y^2| < 16\right \}$$ is given by

What is the Cartesian product of $$A = \left \{1, 2\right \}$$ and $$B = \left \{a, b\right \}$$?

Given that $$f\left( x \right) =5{ x }^{ 2 }-8x,g\left( x \right) ={ x }^{ 2 }-5x-24$$. Find $$\left( \displaystyle\frac { f }{ g }  \right) \left( x \right) $$

Find $$\left( f.g \right) \left( 2 \right) $$ when $$f\left( x \right) =x-1$$ and $$g\left( x \right) =-5{ x }^{ 2 }+14x+7$$.

 $$(x, y)$$ and $$(p, q)$$ are two ordered pairs. Find the values of $$p$$ and $$y$$, if $$(4y + 5, 3p - 1) = (25, p + 1)$$

What is the first component of an ordered pair $$(1, -1)$$?

$$(x, y)$$ and $$(p, q)$$ are two ordered pairs. Find the values of $$x$$ and $$p$$, if $$(3x - 1, 9) = (11, p + 2)$$