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

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

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Q. Given that f(x)=2x,g(x)=x−2 f(x)=2 x, g(x)=x-2 and h(x)=−3f(x+3)−g(x) h(x)=-3 f(x+3)-g(x) , then what is the value of h(1) h(1) ?\newlineAnswer:
  1. Write Functions Given: First, let's write down the functions given:\newlinef(x)=2xf(x) = 2x\newlineg(x)=x−2g(x) = x - 2\newlineh(x)=−3f(x+3)−g(x)h(x) = -3f(x + 3) - g(x)\newlineWe need to find the value of h(1)h(1).
  2. Find f(4)f(4): Now, let's find the value of f(x+3)f(x + 3) when x=1x = 1.\newlinef(1+3)=f(4)=2×4=8f(1 + 3) = f(4) = 2 \times 4 = 8
  3. Calculate g(1)g(1): Next, we calculate the value of g(x)g(x) when x=1x = 1.\newlineg(1)=1−2=−1g(1) = 1 - 2 = -1
  4. Substitute Values into h(x)h(x): Now we can substitute the values of f(4)f(4) and g(1)g(1) into the equation for h(x)h(x) to find h(1)h(1).
    h(1)=−3f(1+3)−g(1)h(1) = -3f(1 + 3) - g(1)
    h(1)=−3×8−(−1)h(1) = -3 \times 8 - (-1)
    h(1)=−24+1h(1) = -24 + 1
  5. Simplify to Find h(1)h(1): Finally, we simplify the expression to find the value of h(1)h(1).\newlineh(1)=−24+1=−23h(1) = -24 + 1 = -23

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