If the graph of the function f(x)=ax−1xn(ax+1) is  symmetrical about the y -axis, then n equal

To determine the value of n that makes the graph of the function f(x) = (ax - 1)/(xn(ax + 1)) symmetrical about the y-axis, we can use the property of symmetry.

A function is symmetrical about the y-axis if and only if replacing x with -x in the function equation results in an equivalent expression.

Let's apply this property to the given function:

f(-x) = a(-x) - 1 / n(-x)(a(-x) + 1) = -ax - 1 / -nx(-ax + 1) = (ax + 1) / (nx(ax - 1))

Now, we need to compare this expression with the original function f(x) = (ax - 1)/(xn(ax + 1)).

By comparing the two expressions, we can see that they are equivalent if and only if the numerators and denominators are the same.

Equating the numerators: ax + 1 = ax - 1

Simplifying the equation: 1 = -1

This equation is not possible, which means that the numerators cannot be equal.

Therefore, there is no value of n that makes the graph of the function f(x) = (ax - 1)/(xn(ax + 1)) symmetrical about the y-axis.