Question 402167: Please help with the following:
1. Is the graph of f(x) = x^1171−5x^109 +3 y-axis symmetirc, origin symmetric, or neither one. Explain your answer.
2. If f(x)= x+2 over x^2+1 and g(x) = 2 over x, determine f(3), g(3), (f + g)(3), (f − g)(3), (fg)(3), (f over g) (3), f ◦ g(3), and g ◦ f(3).
4. If f(x)= 2x-3 over 4x+5, detemine a formula for f^-1(x).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Is the graph of f(x) = x^1171−5x^109 +3 y-axis symmetirc, origin symmetric, or neither one. Explain your answer.
f(-x) = (-x)^1171-5(-x)^109
= -x^1171+5x^109
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-f(-x) = x^1171-5x^109
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Since f(-x) is not equal to f(x) f is not y-axis symmetric.
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Since -f(-x) equals f(x) f is origin symmetric.
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2. If f(x)= x+2 over x^2+1 and g(x) = 2 over x, determine f(3), g(3), (f + g)(3), (f − g)(3), (fg)(3), (f over g) (3), f ◦ g(3), and g ◦ f(3).
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You'll have to try those yourself and post your answers for review.
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4. If f(x)= 2x-3 over 4x+5, detemine a formula for f^-1(x).
1st: Interchange x and y to get:
x = (2y-3)/(4y+5)
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2nd: Solve for "y":
4xy+5x = 2y-3
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2y-4xy = 5x+3
(2-4x)y = 5x+3
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y = (5x+3)/(2-4x)
That is f^-1(x)
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Cheers,
Stan H.
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