Question 250697: if f(x) = 3^(2 - 3x)
then the value of [f(1 + x)][f(1 - x)] is....?
Thanks, please show steps and explain!
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! Here is the original equation:
(i) f(x) = 3^(2 - 3x)
We want
first, [f(1 + x)]
wherever you see x replace it with 1 + X. We get
f(1 + X) = 3^(2 - 3*(1 + X))
(ii) f(1 + X) = 3^(-3X - 1)
Second, [f(1 - x)]
wherever you see x replace it with 1 - X. We get
f(1 - X) = 3^(2 - 3*(1 - X))
(iii) f(1 - X) = 3^(3X - 1)
Now, we multiply (ii) and (iii) to get
(iv) [f(1 + X)][f(1 - X)] = 3^(-3X - 1) * 3^(3X - 1)
Since the bases are the same, we just add the exponents. We get
(v) [f(1 + X)][f(1 - X)] = 3^(-2) = 1/9.
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