Question 1004226: If (f*g)(x)= x^2-6x+8 and g(x)= x-3 , which expression could represent f(x)?
a. x – 4
b. x – 1
c. x^2 - 1
d. x^2 - 6x +5
When they don't give you a value to input as x, do you just multiply the two equations together?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The problem would be written as f * g or f(x) * g(x) if you multiplied to find the answer.
However, the problem is written (f*g)(x) which is the composite function. In order to do this, you apply g first and then f.
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We are given the composite function,
(f*g)(x) = x^2 -6x + 8 and g(x) = x-3 and
4 possibilities for f(x),however, we know there has to be an x^2 term in f(x) since there is an x^2 term in the composite - therefore we need only check c and d, let's check them by substituting x-3 for x in each possibility
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c) (x-3)^2 - 1 = x^2 -6x +9 - 1 = x^2 -6x +8
therefore c is the answer, but let's check d also
d) (x-3)^2 -6(x-3) + 5 = x^2 -6x +9 -18x +18 +5 = x^2 -24x +32
d does not give us the composite function
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c is the answer
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