Show that the function `f : R rarr R` defined by f(x) = cos (5x+3) is neither one-one not onto.

Explanation

To show that the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = \cos(5x + 3) \) is neither one-one nor onto, we will analyze the properties of the function step by step.

### Step 1: Check if the function is one-one

A function is one-one (injective) if for any two different inputs, the outputs are also different. Mathematically, this means if \( f(x_1) = f(x_2) \), then it must follow that \( x_1 = x_2 \).

1. Assume \( f(x_1) = f(x_2) \).
\[
...