Question 747293: Let f(x) = 4x - 7 and g(x) = 2x - 3. Find.
(f*g)(4)
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! Let f(x) = 4x - 7 and g(x) = 2x - 3. Find.
(f*g)(4)
All we need to do is plug what f and g are into the multiplication problem. In terms of x (when x is in the domain of f and g), (f*g) is
(4x-7)(2x-3).
Multiplying this out, we have
(4x-7)(2x-3) = 8x^2 - 26x + 21.
Since there is another factor, 4, being multiplied or multiplying in the problem, we need to multiply what we have just found by that number:
(8x^2 - 26x + 21)(4) = 32x^2 - 104x + 84.
Combining all of these parts, we can see the entire picture in the next series of steps:
(f*g)(4) = (4x-7)(2x-3)(4) = (8x^2-26x+21)(4) = 32x^2 - 104x + 84.
We could also multiply 4 and (4x-7) or 4 and (2x-3) first and then proceeded to multiply the rest of the problem. No matter which two sets of parentheses you start with, the final answer should be the same.
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