Give a distinguisher to differentiate between PRP and RPO
As you do not specify what the domain of the function is, I'm going to assume that we're talking about functions of the form $f:\{0,1\}^n \to \{0,1\}^n$.

The distinguisher works as follows:


Let $q(n)$ be some polynomial.
Choose $q(n)$ many distinct elements from $\{0,1\}^n$. Call them $x_1,\dots,x_q$.
Query each $x_i$ to the oracle and record the result as $y_i$.
If there exists any $y_i=y_j$ with $i\neq j$, output $0$, otherwise output $1$.


If the oracle is a PRP, then it is by definition a permutation (i.e. has no collisions) and since $x_i\neq x_j$ for all $i\neq j$ the distinguisher outputs $1$ with probability $1$.

If the oracle is a truly random function, then each $y_i$ is uniformly and independently distributed. The probability that there is at least one collision among $q(n)$ randomly sampled elements of $\{0,1\}^n$ is $$1-\prod_{i=1}^{q(n)}\frac{2^n-i}{2^n} \geq 1$$ and therefore the distinguisher will output $1$ with probability $1-\varepsilon(n)$ for some $\varepsilon(n)\geq0$.