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# help

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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

#1
+5768
+2

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

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

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May 9, 2019

#1
+5768
+2
$$f(x) \text{ is even, so }f(-x)=f(x)$$
$$g(2)=f(2+3)-5 = f(5)-5=-2\\ f(-5)=f(5)\\ f(-5)-5=-2\\ f(-8+3)-5 = -2\\ g(-8)=-2\\ (a,b)=(-8,-2)$$