Suppose \(f(x)\) is a function defined for all real x, and suppose f is invertible (that is, \(f^{-1}(x)\)exists for all x in the range of f). If the graphs of \(y=f(x^2)\) and \(y=f(x^4)\) are drawn, at how many points do they intersect?
\(f(x) \text{ being invertible means that if }f(x)=f(y) \text{ then }x=y\\ \text{so we are looking for points where }x^2 = x^4\\ \text{Can you determine for which values of }x, ~x^2 = x^4 ~?\)
