Question

You have two exponential functions. One function has the formula g(x) = 3(2 x ). The other function has the formula h(x) = 2 x+1. Which option below gives formula for k(x) = (g – h)(x)?
A) k(x) = 2x
B) k(x) = 5(2x)
C) k(x) = 5(2x+1)
D) k(x) = 2

Answer 1

Given two exponential functions:
$g(x)=3(2^x)$ and $h(x)=2^{x+1}$

$k(x) = (g-h)(x)$ is given by
$k(x)=g(x)-h(x) \\ \\ =3(2^x)-2^{x+1}=3(2^x)-2(2^{x}) \\ \\ =2^x(3-2)=2^x$

Therefore, the option that gives the formula for k(x) = (g - h)(x) is option A.
$k(x)=2^x$