Relations and F...

If $$f(x)=\dfrac{x+1}{x-1}$$ and $$g(x)=2x-1, f[g(x)]=$$

In the set of integers under the operation $$\ast $$ defined by $$a\ast b=a+b-1$$, the identity element is:

The number of onto functions from the set $$\{1, 2, .........., 11\}$$ to set $$\{1, 2, ....., 10\}$$ is

Which of the following is not a binary operation on $$R$$?

The number of real linear functions $$f(x)$$ satisfying $$f(f(x))=x+f(x)$$ is

Consider the function $$f(x)=\displaystyle\frac{x-1}{x+1}$$. What is $$f(f(x))$$ equal to?

Let N denote the set of all non-negative integers and Z denote the set of all integers. The function $$ f : Z \rightarrow N$$ given by f(x) = |x| is :

If $$N$$ is a set of natural numbers, then under binary operation $$a\cdot b = a + b, (N, .)$$ is

If $$f(x) = \log_{e}\left (\dfrac {1 + x}{1 - x}\right ), g(x) = \dfrac {3x + x^{3}}{1 + 3x^{2}}$$ and $$go f(t) = g(f(t))$$, then what is $$go f\left (\dfrac {e - 1}{e + 1}\right )$$ equal to?

If $$g(x)=\dfrac{1}{f(x)}$$ and $$f(x)=x, x\ne 0,$$ then which one of the following is correct?