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Let \(f(x)\) be an even function defined for all real numbers \(x,\) and let \(g(x) = f(x + 3) - 5.\) You are told that the graph of $y = g(x)$ passes through the point \((2,-2)\). Then the graph of \(y=g(x)\) must also pass through the point \((a,b).\) . Find \((a,b).\) 

 May 9, 2019

Best Answer 

 #1
avatar+6046 
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\(f(x) \text{ is even, so }f(-x)=f(x)\)

 

\(g(2)=f(2+3)-5 = f(5)-5=-2\\ f(-5)=f(5)\\ f(-5)-5=-2\\ f(-8+3)-5 = -2\\ g(-8)=-2\\ (a,b)=(-8,-2)\)

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 May 9, 2019
 #1
avatar+6046 
+2
Best Answer

\(f(x) \text{ is even, so }f(-x)=f(x)\)

 

\(g(2)=f(2+3)-5 = f(5)-5=-2\\ f(-5)=f(5)\\ f(-5)-5=-2\\ f(-8+3)-5 = -2\\ g(-8)=-2\\ (a,b)=(-8,-2)\)

Rom May 9, 2019

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