Show that the function f (x) = ax, a > 1 is strictly increasing on R.

Asked by Topperlearning User | 6th Aug, 2014, 09:18: AM

Expert Answer:

Let x1, x2 Î R such that x­1 < x2. Then,

x1 < x2

=> ax1 < ax2 [Since a>1 also, x1>x2 =>ax1 > ax2

=> f (x1) < f (x2)

Thus, x1, x2 Þ f(x1) < f(x2) for all x1, x2 ΠR

Hence, f (x) is strictly increasing function on R

Answered by  | 6th Aug, 2014, 11:18: AM