Solution:

It is given that $f: \mathbf{R} \rightarrow \mathbf{R}$ is defined as $f(x)=10 x+7 .$

One-one:

Let $f(x)=f(y)$, where $x, y \in \mathbf{R}$.

$\Rightarrow 10 x+7=10 y+7 \\ $

$\Rightarrow x=y \\ $

$\therefore f$ is a one-one function.

Onto:

For $y \in \mathbf{R} \\ $

let …