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

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

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Full solution

Q. Given that f(x)=x−1,g(x)=3x f(x)=x-1, \quad g(x)=3 x and h(x)=f(x−1)+3g(x−2) h(x)=f(x-1)+3 g(x-2) , then what is the value of h(1) h(1) ?\newlineAnswer:
  1. Find f(x−1)f(x-1) at x=1x=1: First, we need to find the value of f(x−1)f(x-1) when x=1x=1.
    f(x)=x−1f(x) = x - 1
    f(1−1)=f(0)=0−1=−1f(1 - 1) = f(0) = 0 - 1 = -1
  2. Calculate g(x−2)g(x-2) at x=1x=1: Next, we calculate the value of g(x−2)g(x-2) when x=1x=1.
    g(x)=3xg(x) = 3x
    g(1−2)=g(−1)=3(−1)=−3g(1 - 2) = g(-1) = 3(-1) = -3
  3. Find 3g(x−2)3g(x-2) at x=1x=1: Now, we need to find the value of 3g(x−2)3g(x-2) when x=1x=1. \newline3g(x−2)=3×g(−1)=3×(−3)=−93g(x-2) = 3 \times g(-1) = 3 \times (-3) = -9
  4. Find h(x)h(x) at x=1x=1: Finally, we can find the value of h(x)h(x) when x=1x=1.
    h(x)=f(x−1)+3g(x−2)h(x) = f(x-1) + 3g(x-2)
    h(1)=f(0)+3g(−1)=−1+(−9)=−10h(1) = f(0) + 3g(-1) = -1 + (-9) = -10

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