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Integrations and complex functions Integrations and complex functions ,Let π(π₯) = βπ₯ β 3 and π(π₯) = (π₯ β 3)2, find (πππ)(7). solutions Answer: gof (7) = 1 f (7) = βx-3 =β4 =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 π(π₯) = βπ₯ β 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 donβt repeat. I have used a f(x)= x+1 as my reference equation.Β solution Answer:
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Variables and Squares, See the working belowΒ for the problem. Solve: 3β(6π₯ + 9) + 8 = 5 Solution Answers: x= -6. Work: 3β6π₯ + 9Β Β + 8 = 5 3β6π₯Β + 9 = 5β8 Β Β Β Β Β Β Β Β 3β6π₯Β + 9 = β3. We cube both sides 6 π₯Β +9 = -27 6 π₯Β = β36 π₯Β = β6 Variables and
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Mathematics: Laws of Logarithms, Evaluate the expression: πππ1/5(1) Mathematics: Logarithms and calculus , Evaluate the expression: πππ1/5(1) solution Answer: log1/5 (1) = 0. Work: Law of logs says, the Log of 1 to any base is 0. LINK N.B law of logarithmshttps://libguides.csudh.edu/citation/apa-7 Evaluate the expression: πππ1/5(1) Mathematics: Logarithms and calculus
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Squares and square roots: Equations Find the real value(s) of x that verify: βπ₯ + β7π₯ + 2 = 0 solution Answer: NO REAL VALUES. Work: Let βπ₯ be a and β (7x +2) be b If a>=0, b>=0 thenβπ₯ (a) + β (7x +2)(b)=0, Then a=b=0, for this equation to be
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Basic math: Mathematics, Expressions, Indices and Logarithms Evaluate the expression: πππ82 solution Answers: x =1/3 Work: rewrite the log to express the unknown value of x Log82 =x Remove the log, 8x=2 the we solve this by reducing 8 to base 2. Therefore, 8x=2 becomes 2(3)x =21 . the bases are the same
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Domain functions and Algorithms : Find the domain of the function: π(π₯) = πππ4 (4 β 3π₯). solutions Answer: x= 4/3, so the domain is (4/3, β) Work: We identify the argument which 4-3x, argument >0 4-3x>0, solving for x, then -3x>-4 rewrite the domain function, 3x>4 x>4/3 Our domain is {x|x>4/3}
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Problem 3: Solve the equation: (1 β π₯)^3/2 = 8 solution Answer: x= -3 Work: square both sides of the equation. (1-x)3 =64. Then we get the cube root on both sides. (1-x) = 4, we then solve to get the value of x. 1βx = 4. collect the
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Question: Determine the inverse of the function: β(π₯) = 2π₯β3/(1βπ₯) 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 = 2yβ3 1-x Solve for y, x(1βy) = 2yβ3 x-xy= 2yβ3 2y+xy = x +3.
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Subject: Mathematics Quiz Β INSTRUCTIONS Please use the Answer Sheet below to type your work. Problem 1: Solve the equation: (4π₯ β 5)4 = 81. SolutionsΒ Problem 1 Answer: x= 2 or x= 0.5 Work: 4β 4xβ5 = 4 β81. Here, weΒ get the root of 4 on both sides. 4xβ5 =Β±3.
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