We write an inequality:
[tex]f(x) > g(x)[/tex]
[tex]3^x + 3 > 3x + 10[/tex]
[tex]3^x > 3x + 7[/tex]
This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination. [tex]3x+7[/tex] is a linear function while [tex]3^x[/tex] is an exponential one (with limit zero as [tex]x[/tex] approaches [tex]- \infty[/tex]). We see that [tex]3^x = 3x+7[/tex] at approximately [tex]x=2.4[/tex] and [tex]x=-2.3[/tex].
Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at [tex]x=2.42, -2.31[/tex]. By observing our graph, we see that [tex]f(x) > g(x)[/tex] when [tex]x > 2.42[/tex] or [tex]x < -2.31[/tex].
