QPaperGen

Let \(x_1\) and \(x_2\) be any two real numbers such that \(x_1 < x_2\).
Then,

\[f(x_1) = 3x_1 + 17 < 3x_2 + 17 = f(x_2)\]

\[\Rightarrow f(x_1) < f(x_2)\]

Hence, \(f\) is strictly increasing on \(\mathbb{R}\).
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\( \bf Alternate Method:\)

Differentiate the function:

\[f'(x) = \dfrac{d}{dx}(3x + 17) = 3\]

Since \(f'(x) = 3 > 0\) for all \(x \in \mathbb{R}\), the function is strictly increasing on \(\mathbb{R}\).