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Given that f(x)=x-1,quad g(x)=-2x and h(x)=-3f(x)+g(x-3), then what is the value of h(5) ? Answer:

Given that f(x)=x−1,g(x)=−2x f(x)=x-1, \quad g(x)=-2 x and h(x)=−3f(x)+g(x−3) h(x)=-3 f(x)+g(x-3) , then what is the value of h(5) h(5) ?\newlineAnswer:

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Full solution

Q. Given that f(x)=x−1,g(x)=−2x f(x)=x-1, \quad g(x)=-2 x and h(x)=−3f(x)+g(x−3) h(x)=-3 f(x)+g(x-3) , then what is the value of h(5) h(5) ?\newlineAnswer:
  1. Find f(5)f(5): First, we need to find the value of f(5)f(5) since h(x)h(x) involves f(x)f(x).
    f(x)=x−1f(x) = x - 1
    f(5)=5−1=4f(5) = 5 - 1 = 4
  2. Find g(2)g(2): Next, we need to find the value of g(x−3)g(x-3). Since we are evaluating h(5)h(5), we need to find g(5−3)g(5-3).\newlineg(x)=−2xg(x) = -2x\newlineg(5−3)=g(2)=−2×2=−4g(5-3) = g(2) = -2 \times 2 = -4
  3. Calculate h(5)h(5): Now, we can use the values of f(5)f(5) and g(2)g(2) to find h(5)h(5).
    h(x)=−3f(x)+g(x−3)h(x) = -3f(x) + g(x-3)
    h(5)=−3f(5)+g(2)h(5) = -3f(5) + g(2)
    h(5)=−3×4+(−4)h(5) = -3 \times 4 + (-4)
    h(5)=−12−4h(5) = -12 - 4
    h(5)=−16h(5) = -16

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