Problem 1: Find “f(y)”, if

Solution :

Statement of the problem : The given function is a rational function. We have to evaluate the function when independent variable is function itself.

We need to replace “x” by “y”.

Problem 2: Find “f(x)”, if

Solution :

Statement of the problem : The given function is a polynomial function with a polynomial as its argument. We have to evaluate the function for independent variable “x”.

We need to replace “x-1” by “x” in the given equation to find “f(x)”. The right hand side expression, however, does not contain term “x-1”. We, therefore, need to find the term, which will replace “x”. Clearly if "x" replaces "x-1", then "x+1" will replace "x-1+1 = x"

Thus, we need to replace “x” by “x+1”.

Problem 3: If

Solution :

Statement of the problem : The function is a polynomial function. We have to evaluate cube of the function, which involves evaluation of function for arguments, which are independent variable, raised to certain integral powers.

The cube of given function is :

Now,

Hence,

But, we see that :

Hence,

Problem 4: If

Then, find

Solution :

Statement of the problem : The given function is rational function. We have to find the expression which involves (i) function, (ii) function with argument as squared independent variable and (iii) square of the function.

We need to substitute for various terms in the given expression :