2. Show that the function given by f(x) = e^{2x} is increasing on R.

Answers (1)

Let x_1 \ and \ x_2 are two numbers in R
x_1 \ < \ x_2 \Rightarrow 2x_1 < 2x_2 \Rightarrow e^{2x_1} < e^{2x_2} \Rightarrow f(x_1) < f(x_2)
Hence, the function f(x) = e^{2x} is  strictly increasing in R

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