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Given that f(x)=4x,g(x)=x-1 and h(x)=2f(x+3)-2g(x), then what is the value of h(6) ? Answer:

Given that f(x)=4x,g(x)=x−1 f(x)=4 x, 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(6) h(6) ?\newlineAnswer:

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Q. Given that f(x)=4x,g(x)=x−1 f(x)=4 x, 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(6) h(6) ?\newlineAnswer:
  1. Define h(x)h(x): Define the function h(x)h(x) in terms of f(x)f(x) and g(x)g(x).\newlineh(x)=2f(x+3)−2g(x)h(x) = 2f(x+3) - 2g(x)\newlineWe need to find the value of h(6)h(6), so we will substitute xx with 66 in the functions f(x)f(x) and g(x)g(x) later on.
  2. Calculate f(x+3)f(x+3): Calculate f(x+3)f(x+3) when x=6x = 6.\newlinef(x)=4xf(x) = 4x, so f(x+3)=4(x+3)f(x+3) = 4(x+3).\newlineNow substitute xx with 66.\newlinef(6+3)=4(6+3)=4(9)=36f(6+3) = 4(6+3) = 4(9) = 36.
  3. Calculate g(x)g(x): Calculate g(x)g(x) when x=6x = 6.\newlineg(x)=x−1g(x) = x - 1, so g(6)=6−1=5g(6) = 6 - 1 = 5.
  4. Substitute values into h(x)h(x): Substitute the values of f(x+3)f(x+3) and g(x)g(x) into h(x)h(x).
    h(x)=2f(x+3)−2g(x)h(x) = 2f(x+3) - 2g(x).
    Now substitute f(6+3)f(6+3) and g(6)g(6) into h(6)h(6).
    h(6)=2f(6+3)−2g(6)=2(36)−2(5)=72−10=62h(6) = 2f(6+3) - 2g(6) = 2(36) - 2(5) = 72 - 10 = 62.

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