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

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

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Q. Given that f(x)=3x,g(x)=x+2 f(x)=3 x, \quad g(x)=x+2 and h(x)=−3f(x−2)+2g(x+2) h(x)=-3 f(x-2)+2 g(x+2) , then what is the value of h(3) h(3) ?\newlineAnswer:
  1. Find f(3)f(3): First, we need to find the value of f(x)f(x) when xx is replaced by 33.\newlinef(x)=3xf(x) = 3x\newlinef(3)=3(3)f(3) = 3(3)\newlinef(3)=9f(3) = 9
  2. Find g(3)g(3): Next, we need to find the value of g(x)g(x) when xx is replaced by 33.
    g(x)=x+2g(x) = x + 2
    g(3)=3+2g(3) = 3 + 2
    g(3)=5g(3) = 5
  3. Find f(1)f(1): Now, we need to find the value of f(x−2)f(x-2) when xx is replaced by 33.
    f(x−2)=3(x−2)f(x-2) = 3(x-2)
    f(3−2)=3(3−2)f(3-2) = 3(3-2)
    f(1)=3(1)f(1) = 3(1)
    f(1)=3f(1) = 3
  4. Find g(5)g(5): We also need to find the value of g(x+2)g(x+2) when xx is replaced by 33.
    g(x+2)=(x+2)+2g(x+2) = (x+2) + 2
    g(3+2)=(3+2)+2g(3+2) = (3+2) + 2
    g(5)=5+2g(5) = 5 + 2
    g(5)=7g(5) = 7
  5. Calculate h(3)h(3): Now we can calculate h(x)h(x) using the values of f(x−2)f(x-2) and g(x+2)g(x+2) we found.\newlineh(x)=−3f(x−2)+2g(x+2)h(x) = -3f(x-2) + 2g(x+2)\newlineh(3)=−3f(1)+2g(5)h(3) = -3f(1) + 2g(5)\newlineh(3)=−3(3)+2(7)h(3) = -3(3) + 2(7)\newlineh(3)=−9+14h(3) = -9 + 14\newlineh(3)=5h(3) = 5

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