Question 202867: One of the tutors pleaseeee pleaseee help me with the following Advanced Functions question. I would be greatly thankful.
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?(3 marks:1 mark each)
a)y=(2)*(3^x+2)-(3)
b)y=3^2x+1
c)y=(1/27)*(3^2x)+(2)
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! f(x) =3^x,,,,,g(x) = (x+2),,,,,,h(x) = (2x-3)
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(a) y= h[g{f(x)}] = h[{ (3^x) +2 }] = 2[3^x +2] -3
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(b) y = f[h{g(x)}] = f[ 2{x+2} -3]=f[2x+4-3] = f[2x+1] = 3^(2x+1)
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(c) y= g[f{h(x)}]= g[3^{2x-3}]=[{3^(2x-3)} +2] ={3^2x-3^-3} +2 =
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3^(2x)/3^3+2=1/27*3^(2x) +2
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