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Given that f(x)=x+3,quad g(x)=-4x and h(x)=-3f(x)+3g(x+1), then what is the value of h(6) ? Answer:

Given that f(x)=x+3,g(x)=−4x f(x)=x+3, \quad g(x)=-4 x and h(x)=−3f(x)+3g(x+1) h(x)=-3 f(x)+3 g(x+1) , then what is the value of h(6) h(6) ?\newlineAnswer:

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Q. Given that f(x)=x+3,g(x)=−4x f(x)=x+3, \quad g(x)=-4 x and h(x)=−3f(x)+3g(x+1) h(x)=-3 f(x)+3 g(x+1) , then what is the value of h(6) h(6) ?\newlineAnswer:
  1. Find f(6)f(6) Calculation: First, we need to find the value of f(6)f(6) using the function f(x)=x+3f(x) = x + 3.\newlineCalculation: f(6)=6+3=9f(6) = 6 + 3 = 9.
  2. Find g(7)g(7) Calculation: Next, we need to find the value of g(x)g(x) at x+1x + 1, which means we need to calculate g(6+1)g(6 + 1) or g(7)g(7) using the function g(x)=−4xg(x) = -4x.\newlineCalculation: g(7)=−4×7=−28g(7) = -4 \times 7 = -28.
  3. Substitute into h(x)h(x): Now, we can substitute the values of f(6)f(6) and g(7)g(7) into the function h(x)=−3f(x)+3g(x+1)h(x) = -3f(x) + 3g(x + 1).\newlineCalculation: h(6)=−3×f(6)+3×g(7)=−3×9+3×(−28)h(6) = -3 \times f(6) + 3 \times g(7) = -3 \times 9 + 3 \times (-28).
  4. Calculate h(6)h(6): Perform the multiplication and addition to find the value of h(6)h(6).\newlineCalculation: h(6)=−3×9+3×(−28)=−27+(−84)=−27−84=−111h(6) = -3 \times 9 + 3 \times (-28) = -27 + (-84) = -27 - 84 = -111.

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