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Given that f(x)=x-4,quad g(x)=-3x and h(x)=-f(x)+2g(x-1), then what is the value of h(7) ? Answer:

Given that f(x)=x−4,g(x)=−3x f(x)=x-4, \quad g(x)=-3 x and h(x)=−f(x)+2g(x−1) h(x)=-f(x)+2 g(x-1) , then what is the value of h(7) h(7) ?\newlineAnswer:

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Q. Given that f(x)=x−4,g(x)=−3x f(x)=x-4, \quad g(x)=-3 x and h(x)=−f(x)+2g(x−1) h(x)=-f(x)+2 g(x-1) , then what is the value of h(7) h(7) ?\newlineAnswer:
  1. Find f(7)f(7): First, we need to find the value of f(7)f(7) using the function f(x)=x−4f(x) = x - 4.\newlineCalculation: f(7)=7−4=3f(7) = 7 - 4 = 3
  2. Calculate g(x−1)g(x-1): Next, we need to find the value of g(x−1)g(x-1) when x=7x = 7. This means we need to calculate g(7−1)g(7-1) or g(6)g(6).\newlineCalculation: g(6)=−3×6=−18g(6) = -3 \times 6 = -18
  3. Determine h(x)h(x): Now, we need to find the value of h(x)h(x) using the given expression h(x)=−f(x)+2g(x−1)h(x) = -f(x) + 2g(x-1). We will substitute xx with 77 and use the values we found for f(7)f(7) and g(6)g(6).\newlineCalculation: h(7)=−f(7)+2g(6)=−(3)+2(−18)=−3−36=−39h(7) = -f(7) + 2g(6) = -(3) + 2(-18) = -3 - 36 = -39

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