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Let f(x)= ||x+2|-3|. If' a' denotes the ...

Let `f(x)= ||x+2|-3|.` If' `a'` denotes the number of local minima, `'b'` denotes the number of local maxima and `'c'` denotes the product of roots of `f(x) = 0,` then `a + 2b-c ` is

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To solve the problem step by step, we need to analyze the function \( f(x) = ||x + 2| - 3| \) and determine the values of \( a \), \( b \), and \( c \). ### Step 1: Analyze the Inner Function First, we consider the inner function \( |x + 2| \). This function is defined as: - \( x + 2 \) when \( x + 2 \geq 0 \) (i.e., \( x \geq -2 \)) - \( -(x + 2) \) when \( x + 2 < 0 \) (i.e., \( x < -2 \))
To solve the problem step by step, we need to analyze the function \( f(x) = ||x + 2| - 3| \) and determine the values of \( a \), \( b \), and \( c \). ### Step 1: Analyze the Inner Function First, we consider the inner function \( |x + 2| \). This function is defined as: - \( x + 2 \) when \( x + 2 \geq 0 \) (i.e., \( x \geq -2 \)) - \( -(x + 2) \) when \( x + 2 < 0 \) (i.e., \( x < -2 \))
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