I want to find the invariant points( points that are fixed) algrebraically of x^2 - 25 and its reciprocal. Would I set up my equation like this?

Question

0 = x^2 -25

or

0 = 1/ x^2 - 25

Thanks

Answer 1

Knowing the definition of specific math terms helps solving the problem, most of the time.

Here the term is invariant point, which is usually called fixed point, defined as follows (Wiki)
"In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function. That is to say, c is a fixed point of the function f(x) if and only if f(c) = c."

So invariant points can be solved by equating f(x)=x, in the given case,
x²-25=x
x²-x-25=0
Solve for x using the quadratic formula.