Prove that e x ≥ 1 + x if x ≥ 0.

Answer 1

ex is greater than 1, if x is greater than zero

that must mean

e^x > 1 if x>0

any number to the 0 power = 1

e^0 = 1

any number to a power greater than zero will be greater than 1

graph e^x

for x<0 all e^x <1

for all x>0 e^x>1

same resutl for any variable a^x for a>0, x>0