At which x value will f(x)=3x+3 exceed g(x)=3x+10

Question

asked Jul 5, 2018 67.7k views

2 Answers

VKen · Answer 1 · 2018-07-08T07:33:57+0000

there are no x value that allows f(x) to exceed g(x). f(x) is parallel to g(x) and it will always be 7 less than g(x).

VPP · Answer 2 · 2018-07-11T10:53:45+0000

We write an inequality:

f(x) > g(x)

This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination.
3x+7

is a linear function while
3^x

is an exponential one (with limit zero as

approaches
$- \infty$ ). We see that
3^x = 3x+7

at approximately
x=2.4

and

.

Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at
x=2.42, -2.31

. By observing our graph, we see that
f(x) > g(x)

when

or

.