The inequality 2 x1 is true for all positive real numbers x

The inequality 2 x+1 is true for all positive real numbers x. If a statement is true, prove it. If a statement is false, disprove it.

Solution

this assumption is absolutely true , a better way to prove this can be using graph .

a graph of an exponential function is always above than a polynomial function hence we can definitely conclude

that the relation always holds. since when a graph is upper than its counterpart that means its y value is always greater.

another way can be if try to find the rate of change of each curve and then can make a comment