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

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

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Q. Given that f(x)=−3x,g(x)=x+1 f(x)=-3 x, \quad g(x)=x+1 and h(x)=2f(x−3)−2g(x) h(x)=2 f(x-3)-2 g(x) , then what is the value of h(3) h(3) ?\newlineAnswer:
  1. Find f(0)f(0): First, we need to find the value of f(x)f(x) when xx is replaced by (3−3)(3-3), which is f(0)f(0).\newlinef(x)=−3xf(x) = -3x\newlinef(0)=−3(0)=0f(0) = -3(0) = 0
  2. Calculate g(3)g(3): Next, we calculate the value of g(x)g(x) when xx is replaced by 33.
    g(x)=x+1g(x) = x + 1
    g(3)=3+1=4g(3) = 3 + 1 = 4
  3. Substitute values into h(x)h(x): Now, we can substitute the values of f(0)f(0) and g(3)g(3) into the equation for h(x)h(x).
    h(x)=2f(x−3)−2g(x)h(x) = 2f(x-3) - 2g(x)
    h(3)=2f(3−3)−2g(3)=2f(0)−2g(3)h(3) = 2f(3-3) - 2g(3) = 2f(0) - 2g(3)
    h(3)=2(0)−2(4)=0−8=−8h(3) = 2(0) - 2(4) = 0 - 8 = -8

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