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Find g(x), where g(x) is the reflection across the y-axis of f(x)=–2|x+3|+5.

Question

Find g(x), where g(x) is the reflection across the y-axis of f(x)=–2|x+3|+5.

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Solution

To find g(x), the reflection of f(x) across the y-axis, we need to replace every x in the function f(x) with -x.

The function f(x) is given as f(x) = -2|x+3|+5.

So, to find g(x), we replace x with -x in f(x):

g(x) = -2|-x+3|+5.

This is the function g(x), which is the reflection of f(x) across the y-axis.

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