$(a)$ $\left(x^2-v t\right)^2$
$(b)$ $\log \left[\frac{(x+v t)}{x_0}\right]$
$(c)$ $e^{\left\{-\frac{(x+v t)}{x_0}\right\}^2}$
$(d)$ $\frac{1}{x+v t}$
The only function in the given function which is not of the form $f(k x-\omega t)$ is the first one $(a)$ Hence option $(a)$ is correct.
