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Question 694521: find the requested composition of functions. 4x^2+5x+4 and g(x)=5x-7 find (g f)(x)
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! I'm presuming that the expression 4x^2+5x+4 is the function f(x) and functions g and f are being represented in multiplication in (gf). Here we have two functions, f(x) and g(x), that are being expressed in solvable notation (gf)(x). This is actually a shorthand method of saying f(x) and g(x) are undergoing an operation together. That is, whatever sign is between the letters f and g in the parentheses, that is the operation that is taking effect on both of the functions. If they are being added together in parentheses, then all of their terms are being added together. If subtraction, then they're being subtracted. The same is with division. I'm reading this problem as if they are being multiplied together since there is no sign between f and g in the parentheses. If the letters are next to each other with no sign, it would mean multiplication. It's the same idea as 3x or 4√2 in the sense that both items represent multiplication between its parts (3 times x and 4 times √2). All (gf)(x) means is that both functions are being multiplied together. So,
(gf)(x)
f(x) * g(x)
(4x^2+5x+4)*(5x-7)
20x^3-28x^2+25x^2-35x+20x-28
20x^3-3x^2-15x-28.
(gf)(x) = 20x^3-3x^2-15x-28. You must keep in mind if you are in a higher math course that these functions must be continuous. Usually in algebra 1 this is not an issue since discontinuity is not discussed in depth.
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