The function $f\left(x\right)=\cos \left(3x-4\right)$defined from the set of real numbers R to R, then the function $f\left(x\right)$ is 

The given function is $f\left(x\right)=\cos \left(3x-4\right)$

Given that the domain and codomain both are equal to set of real numbers R

The cosine function is one one and onto only when domain is $\left[0,\pi \right]$ and range is $\left[-1,1\right]$

But the given domain is super set of $\left[0,\pi \right]$ and the codomain is not equal to range

For $x=\frac{4}{3},\frac{2\pi +4}{3}$, the images are same, so the function is not one one

For $2\in R$ there is no $x\in R$ such that $\cos \left(3x-4\right)=2$, so that it is not onto.

Therefore, the funciton $f\left(x\right)=\cos \left(3x-4\right)$ is neither one one nor onto.