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Given that f(x)=3x,g(x)=x+4 and h(x)=-2f(x+3)-2g(x-3), then what is the value of h(6) ? Answer:

Given that f(x)=3x,g(x)=x+4 f(x)=3 x, g(x)=x+4 and h(x)=−2f(x+3)−2g(x−3) h(x)=-2 f(x+3)-2 g(x-3) , then what is the value of h(6) h(6) ?\newlineAnswer:

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Q. Given that f(x)=3x,g(x)=x+4 f(x)=3 x, g(x)=x+4 and h(x)=−2f(x+3)−2g(x−3) h(x)=-2 f(x+3)-2 g(x-3) , then what is the value of h(6) h(6) ?\newlineAnswer:
  1. Define Functions: Define the functions f(x)f(x), g(x)g(x), and h(x)h(x) as given.f(x)=3xf(x) = 3xg(x)=x+4g(x) = x + 4h(x)=−2f(x+3)−2g(x−3)h(x) = -2f(x + 3) - 2g(x - 3)
  2. Calculate Values: Calculate f(x+3)f(x + 3) and g(x−3)g(x - 3) for x=6x = 6.
    f(6+3)=f(9)=3×9=27f(6 + 3) = f(9) = 3 \times 9 = 27
    g(6−3)=g(3)=3+4=7g(6 - 3) = g(3) = 3 + 4 = 7
  3. Substitute Values: Substitute the values of f(9)f(9) and g(3)g(3) into the h(x)h(x) function.\newlineh(6)=−2×f(9)−2×g(3)h(6) = -2 \times f(9) - 2 \times g(3)\newlineh(6)=−2×27−2×7h(6) = -2 \times 27 - 2 \times 7
  4. Perform Arithmetic Operations: Perform the arithmetic operations to find the value of h(6)h(6).h(6)=−2×27−2×7h(6) = -2 \times 27 - 2 \times 7h(6)=−54−14h(6) = -54 - 14h(6)=−68h(6) = -68

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