Functions Test ...

Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
If $$h(x) = 5f(x) - xg (x)$$, then what is the derivative of $$h(x)$$ ?

The number of non-surjective mappings that can be defined from $$A = \left \{ 1,4,9,16 \right \}  $$ to$$  B=\left \{ 2,8,16,32,64 \right \}$$ is

The number of one-one functions that can be defined from $$A = \left \{ 1,2,3 \right \} $$ to $$  B = \left \{ a,e,i,o,u \right \}$$ is 

If $$A = \left \{ 11, 12, 13, 14 \right \} $$ and $$  B = \left \{ 6,8,9,10 \right \} $$ then the number of bijections defined from $$A$$ to $$B$$ is

If function $$f$$ has an inverse, then which of the following conditions is necessary and sufficient

If $$ f:A\rightarrow B $$ is a constant function which is onto then $$B$$ is

The number of bijection that can be defined from $$A = \left \{ 1,2,8,9 \right \}  $$ to $$  B = \left \{ 3,4,5,10 \right \}$$ is

If $$ f:A\rightarrow B $$ is a bijection then $$ f^{-1} of = $$

Assertion(A): $$ f(x) = \log(x-2)+\log(x-3)$$ and $$ g(x)=\log(x-2)(x-3)$$ then $$ f(x)=g(x)$$

Reason (R): Two functions $$f (x)$$ and $$g (x)$$  are said to be equal if they are defined on the same domain $$A$$ and the co-domain $$B$$ as $$ f(x)=g(x)\forall x \in A$$

Assertion (A) : $$ f(x)=\dfrac{x^{2}-4}{x-2} $$ and $$ g(x) = x+2$$ are equal.

Reason (R): Two functions $$f$$ and $$g$$ are said to be equal if their domains and ranges are equal and $$f(x)=g(x) \forall x \in $$ domain.