Well, I bet you want your answer right away! So here it is.
Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.(f + g)(x) = f (x) + g(x)= [3x + 2] + [4 – 5x]= 3x + 2 + 4 – 5x= 3x – 5x + 2 + 4= –2x + 6(f – g)(x) = f (x) – g(x)= [3x + 2] – [4 – 5x]= 3x + 2 – 4 + 5x= 3x + 5x + 2 – 4= 8x – 2(f × g)(x) = [f (x)][g(x)]= (3x + 2)(4 – 5x)= 12x + 8 – 15x2 – 10x= –15x2 + 2x + 8\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(gf)(x)=g(x)f(x)= \small{\dfrac{3x+2}{4-5x}}=4−5x3x+2My answer is the neat listing of each of my results, clearly labelled as to which is which.( f + g ) (x) = –2x + 6( f – g ) (x) = 8x – 2( f × g ) (x) = –15x2 + 2x + 8\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(gf)(x)=4−5x3x+2
Hope I helped! :) If I did not help that's okay.
-Duolingo