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Integrations and complex functions Integrations and complex functions ,Let ๐(๐ฅ) = โ๐ฅ โ 3 and ๐(๐ฅ) = (๐ฅ โ 3)2, find (๐๐๐)(7). solutions Answer: gof (7) = 1 f (7) = โx-3 =โ4 =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 ๐(๐ฅ) = โ๐ฅ โ 3 […]
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Mathematics: Laws of Logarithms, Evaluate the expression: ๐๐๐1/5(1) Mathematics: Logarithms and calculus , Evaluate the expression: ๐๐๐1/5(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: ๐๐๐1/5(1) Mathematics: Logarithms and calculus
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Basic math: Mathematics, Expressions, Indices and Logarithms Evaluate the expression: ๐๐๐82 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: ๐(๐ฅ) = ๐๐๐4 (4 โ 3๐ฅ). solutions Answer: x= 4/3, so the domain is (4/3, โ) 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 โ ๐ฅ)^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. 1โx = 4. collect the
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