SOLUTION: Given the functions f(x)=3^x, g(x)=x+2, and h(x)=2x-3, what composition of functions would result in each of the following? a) y=2*3^x+2-3 b) y=3^2x+1 C) y=1/27*3^2x+2

SOLUTION: Given the functions f(x)=3^x, g(x)=x+2, and h(x)=2x-3, what composition of functions would result in each of the following? a) y=23^x+2-3 b) y=3^2x+1 C) y=1/273^2x+2

Question 552590: Given the functions f(x)=3^x, g(x)=x+2, and h(x)=2x-3, what composition of functions would result in each of the following?
a) y=2*3^x+2-3
b) y=3^2x+1
C) y=1/27*3^2x+2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given the functions f(x)=3^x, g(x)=x+2, and h(x)=2x-3, what composition of functions would result in each of the following?
a) y=2*3^x+2-3
g[h[f(x)]] = g[h[3^x]] = g[2*3^x-3] = 2*3^x-3+2
===================================================
b) y=3^(2x+1) = (3^x)(3^x)*3 = 3*{f(x)]^2
=========================================

C) y=(1/27)*3^(2x+2) = 3^-3 *3^x(3^x)*3^2 = (1/3)[f(x)]^2
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Cheers,
Stan H.

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