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Integrations and complex functions Integrations and complex functions ,Let 𝑓(𝑥) = √𝑥 − 3 and 𝑔(𝑥) = (𝑥 − 3)2, find (𝑔𝑜𝑓)(7). solutions Answer: gof (7) = 1 f (7) = √x-3 =√4 =2. Work: (gof)(7)= g(f(7))= f(7)= g(2) g(2)= (x-3)2 = (2-3)2 =(-1)2 =1. Integrations and complex functions, Let 𝑓(𝑥) = √𝑥 − 3 […]
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Functions and Vectors Functions and Vectors, Determine is the following function is one-to-one (explain your answer); F = {(-2,1), (-5,-1), (3,-5), (1,-2), (0,5), (-1,6), (-6,7), (7,-6)} solution. APA Answer: ALL FUNCTIONS ARE ONE-IN-ONE. Work: All answers in one-to-one functions don’t repeat. I have used a f(x)= x+1 as my reference equation. solution Answer:
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Variables and Squares, See the working below for the problem. Solve: 3√(6𝑥 + 9) + 8 = 5 Solution Answers: x= -6. Work: 3√6𝑥 + 9 + 8 = 5 3√6𝑥 + 9 = 5–8 3√6𝑥 + 9 = –3. We cube both sides 6 𝑥 +9 = -27 6 𝑥 = –36 𝑥 = –6 Variables and
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Question: Determine the inverse of the function: ℎ(𝑥) = 2𝑥−3/(1−𝑥) Solution and steps followed Answers: f-1 (x)= x+3 2+x Work: we replace h(x) with y, y= 2x-3 1-x We then swap the y for x, x = 2y–3 1-x Solve for y, x(1–y) = 2y–3 x-xy= 2y–3 2y+xy = x +3.
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the solution below is from differential problem
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Solution :Matrices and law of matrices and Squares Question: 1 Since we are told that A is indepented, then we have A2 = A (I – A )2 we expand the problem and then solve (I – A)2 = I2 + A2 – 2AI2 (I– A)2 = I + A –2A
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