Question

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x (input)	f(x) - output
0	-7
4	1
-6	-19
	15

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Explanation:

Step1: Determine the linear function

Assume the function is linear, so \( f(x)=mx + b \). Use two points, e.g., \( (0, -7) \) and \( (4, 1) \). From \( (0, -7) \), we get \( b=-7 \). Then, using \( (4, 1) \): \( 1 = 4m - 7 \), so \( 4m = 8 \), \( m = 2 \). Thus, \( f(x)=2x - 7 \).

Step2: Find x for f(x)=15

Set \( 2x - 7 = 15 \). Add 7 to both sides: \( 2x = 15 + 7 = 22 \). Divide by 2: \( x=\frac{22}{2}=11 \).

Answer:

11