What is the nature of function f(x) = 7x-4 on R?

The correct option is Strictly Increasing.

To determine the nature of the function $f\left(x\right)=7x-4$ on the set of real numbers $R$, we can analyze its derivative.

First, let's find the first derivative of $f\left(x\right)$ with respect to $x$:
$$f^{\text{'}}\left(x\right)=\frac{d}{dx}(7x-4)$$

Applying the basic rules of differentiation, we get:
$$f^{\text{'}}\left(x\right)=7$$

Since the derivative $f^{\text{'}}\left(x\right)=7$ is strictly greater than $0$ for all real numbers $x\in R$, the function is constantly rising as $x$ increases.

By definition, if $f^{\text{'}}\left(x\right)>0$ on an interval, then the function $f\left(x\right)$ is strictly increasing on that interval. Therefore, the function $f\left(x\right)=7x-4$ is strictly increasing on $R$.