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

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

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Full solution

Q. Given that f(x)=−4x,g(x)=x−4 f(x)=-4 x, \quad g(x)=x-4 and h(x)=−f(x−1)+3g(x) h(x)=-f(x-1)+3 g(x) , then what is the value of h(2) h(2) ?\newlineAnswer:
  1. Find f(x)f(x) at x=2x=2: First, we need to find the value of f(x)f(x) when x=2x = 2.
    f(x)=−4xf(x) = -4x
    f(2)=−4×2f(2) = -4 \times 2
    =−8= -8
  2. Calculate g(x)g(x) at x=2x=2: Next, we calculate the value of g(x)g(x) when x=2x = 2.
    g(x)=x−4g(x) = x - 4
    g(2)=2−4g(2) = 2 - 4
    =−2= -2
  3. Find f(x−1)f(x-1) at x=2x=2: Now, we need to find the value of f(x−1)f(x-1) when x=2x = 2.
    f(x−1)=−4(x−1)f(x-1) = -4(x-1)
    f(2−1)=−4(2−1)f(2-1) = -4(2-1)
    =−4(1)= -4(1)
    =−4= -4
  4. Calculate 3g(x)3g(x) at x=2x=2: We also need to calculate 3g(x)3g(x) when x=2x = 2.
    3g(x)=3(x−4)3g(x) = 3(x - 4)
    3g(2)=3(2−4)3g(2) = 3(2 - 4)
    =3(−2)= 3(-2)
    =−6= -6
  5. Find h(x)h(x) using f(x−1)f(x-1) and 3g(x)3g(x) at x=2x=2: Now we can find h(x)h(x) using the values of −f(x−1)-f(x-1) and 3g(x)3g(x) when x=2x = 2.
    h(x)=−f(x−1)+3g(x)h(x) = -f(x-1) + 3g(x)
    h(2)=−(−4)+(−6)h(2) = -(-4) + (-6)
    f(x−1)f(x-1)00
    f(x−1)f(x-1)11

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