Determine the x-intercept of the function:
15. $f(x)=4-|6+2 x|$
The x-intercepts of the function \(f(x) = 4 - |6 + 2x|\) are \(\boxed{x = -1}\) and \(\boxed{x = -5}\)
Step 1 :Set the function equal to zero: \(0 = 4 - |6 + 2x|\)
Step 2 :Rewrite the equation: \(|6 + 2x| = 4\)
Step 3 :This represents two equations: \(6 + 2x = 4\) and \(6 + 2x = -4\)
Step 4 :Solve the first equation: \(6 + 2x = 4\), subtract 6 from both sides to get \(2x = -2\), then divide both sides by 2 to get \(x = -1\)
Step 5 :Solve the second equation: \(6 + 2x = -4\), subtract 6 from both sides to get \(2x = -10\), then divide both sides by 2 to get \(x = -5\)
Step 6 :The x-intercepts of the function \(f(x) = 4 - |6 + 2x|\) are \(\boxed{x = -1}\) and \(\boxed{x = -5}\)