The image $f(T)$ of a maximal split torus $T$ is a split torus of the same dimension, which is contained in a maximal split torus $T'$. But the maximal split tori have the same dimension, and so $f(T)=T'$ (the maximal split tori are even conjugate, see, for example, Milne 2017, 25.10). [I am assuming that, as the question originally stated, that $f$ maps a group to itself. If not, you need to show that the isogenous groups have the same split rank.]

The image $f(T)$ of a maximal split torus $T$ is a split torus of the same dimension, which is contained in a maximal split torus $T'$. But the maximal split tori have the same dimension, and so $f(T)=T'$ (the maximal split tori are even conjugate, see, for example, Milne 2017, 25.10). [I am assuming that, as the question originally stated, $f$ maps a group to itself. Otherwise, you need to use that the two groups have the same split rank.]

The image $f(T)$ of a maximal split torus $T$ is a split torus of the same dimension, which is contained in a maximal split torus $T'$. But the maximal split tori have the same dimension, and so $f(T)=T'$ (the maximal split tori are even conjugate, see, for example, Milne 2017, 25.10).

The image $f(T)$ of a maximal split torus $T$ is a split torus of the same dimension, which is contained in a maximal split torus $T'$. But the maximal split tori have the same dimension, and so $f(T)=T'$ (the maximal split tori are even conjugate, see, for example, Milne 2017, 25.10). [I am assuming that, as the question originally stated, that $f$ maps a group to itself. If not, you need to show that the isogenous groups have the same split rank.]