Given function:
The given function is f(x) = (x^2 + 1)/(ax)

One-to-One Function:
A function is said to be one-to-one if each element in the domain is mapped to a unique element in the range. In other words, no two different elements in the domain can have the same image in the range.

Finding p:
To find the value of p for which the function f(x) is one-to-one, we need to analyze the conditions under which the function is not one-to-one.

Analysis:
Let's assume two different values of x, say x1 and x2, where x1 > p and x2 > p.

If f(x1) = f(x2), then the function is not one-to-one.

Expression for f(x):
f(x) = (x^2 + 1)/(ax)

Substitute x1 and x2 in f(x):
f(x1) = (x1^2 + 1)/(ax)
f(x2) = (x2^2 + 1)/(ax)

Comparing f(x1) and f(x2):
For the function to not be one-to-one, f(x1) = f(x2).

(x1^2 + 1)/(ax) = (x2^2 + 1)/(ax)

Canceling out common terms:
x1^2 + 1 = x2^2 + 1

Subtracting 1 from both sides:
x1^2 = x2^2

Taking square root on both sides:
x1 = x2 or x1 = -x2

Conclusion:
From the above analysis, we can see that for any two different values of x1 and x2, if they satisfy the condition x1 = -x2, then the function will not be one-to-one. This means that the function f(x) is one-to-one if x > p, where p is the value of x for which x = -x.

Finding p:
To find p, we solve the equation x = -x.

x + x = 0
2x = 0
x = 0

Therefore, p = 0.

Explanation:
The given function f(x) = (x^2 + 1)/(ax) is a one-to-one function if x > 0. This means that for any two different values of x1 and x2, where x1 > 0 and x2 > 0, the function will map them to different values in the range. Conversely, if x1 < 0="" and="" x2="" />< 0,="" the="" function="" will="" also="" map="" them="" to="" different="" values="" in="" the="" range.="" however,="" if="" x1="" /> 0 and x2 < 0,="" or="" x1="" />< 0="" and="" x2="" /> 0, the function will not be one-to-one as x1 = -x2. Therefore, the value of p for which the function is one-to-one is 0.