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Given that f(x)=4x,quad g(x)=x+5 and h(x)=-2f(x-2)-2g(x+3), then what is the value of h(2) ? Answer:

Given that f(x)=4x,g(x)=x+5 f(x)=4 x, \quad g(x)=x+5 and h(x)=−2f(x−2)−2g(x+3) h(x)=-2 f(x-2)-2 g(x+3) , then what is the value of h(2) h(2) ?\newlineAnswer:

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Q. Given that f(x)=4x,g(x)=x+5 f(x)=4 x, \quad g(x)=x+5 and h(x)=−2f(x−2)−2g(x+3) h(x)=-2 f(x-2)-2 g(x+3) , then what is the value of h(2) h(2) ?\newlineAnswer:
  1. Given functions and task: Given the functions f(x)=4xf(x) = 4x, g(x)=x+5g(x) = x + 5, and h(x)=−2f(x−2)−2g(x+3)h(x) = -2f(x - 2) - 2g(x + 3), we need to find the value of h(2)h(2). First, we will find the value of f(x−2)f(x - 2) and g(x+3)g(x + 3) when x=2x = 2.
  2. Calculate f(x−2)f(x - 2): Calculate f(x−2)f(x - 2) when x=2x = 2.\newlinef(x−2)=4(x−2)=4(2−2)=4(0)=0f(x - 2) = 4(x - 2) = 4(2 - 2) = 4(0) = 0.
  3. Calculate g(x+3)g(x + 3): Calculate g(x+3)g(x + 3) when x=2x = 2.
    g(x+3)=(x+3)+5=(2+3)+5=5+5=10g(x + 3) = (x + 3) + 5 = (2 + 3) + 5 = 5 + 5 = 10.
  4. Substitute values into h(x)h(x): Now, we will substitute these values into the equation for h(x)h(x).h(x)=−2f(x−2)−2g(x+3)h(x) = -2f(x - 2) - 2g(x + 3).Substitute f(2−2)=0f(2 - 2) = 0 and g(2+3)=10g(2 + 3) = 10 into the equation.h(2)=−2(0)−2(10)=0−20=−20h(2) = -2(0) - 2(10) = 0 - 20 = -20.

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