Question

If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x)?

A. -1
B. 2
C. -3
D. -4

Answer 1

A) x = -1

Explanation:

`f(-1)=3^(-1)=\frac13\\\\g(-1)=2(-1)+5=3\\\\\implies f(x) < g(x)`

`f(2)=3^(2)=9\\\\g(2)=2(2)+5=9\\\\\implies f(x)=g(x)`

`f(-3)=3^(-3)=(1)/(27)\\\\g(-3)=2(-3)+5=-1\\\\\implies f(x) > g(x)`

`f(-4)=3^(-4)=(1)/(81)\\\\g(-4)=2(-4)+5=-3\\\\\implies f(x) > g(x)`