7. \( f(x)=|x+1| \) and \( g(x)=2 x-9 \) a) \( f(-10) \) b) \( g(x)=21 \) c) \( f(-3)+g(2) \)
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To solve the given functions, let's break it down step by step. First, we find \( f(-10) \): - \( f(x) = |x + 1| \) - So, \( f(-10) = |-10 + 1| = |-9| = 9 \). Next, we solve \( g(x) = 21 \): - Given \( g(x) = 2x - 9 \), we set it equal to 21: \[ 2x - 9 = 21 \\ 2x = 30 \\ x = 15 \] Finally, we calculate \( f(-3) + g(2) \): - For \( f(-3) \): \[ f(-3) = |-3 + 1| = |-2| = 2 \] - For \( g(2) \): \[ g(2) = 2(2) - 9 = 4 - 9 = -5 \] - So, \( f(-3) + g(2) = 2 + (-5) = 2 - 5 = -3 \). In summary: a) \( f(-10) = 9 \) b) \( g(x) = 21 \) gives \( x = 15 \) c) \( f(-3) + g(2) = -3 \)
