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

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

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Q. Given that f(x)=x−4,g(x)=5x f(x)=x-4, \quad g(x)=5 x and h(x)=2f(x−3)+2g(x−2) h(x)=2 f(x-3)+2 g(x-2) , then what is the value of h(4) h(4) ?\newlineAnswer:
  1. Identify Functions and Composition: Identify the functions and the composition.\newlineWe are given three functions f(x)f(x), g(x)g(x), and h(x)h(x), where h(x)h(x) is a composition of f(x)f(x) and g(x)g(x). We need to find the value of h(4)h(4).
  2. Calculate f(x−3)f(x-3): Calculate f(x−3)f(x-3) when x=4x=4.\newlinef(x)=x−4f(x) = x - 4, so f(x−3)=(x−3)−4=x−7f(x-3) = (x-3) - 4 = x - 7.\newlineNow, substitute xx with 44: f(4−3)=4−7=−3f(4-3) = 4 - 7 = -3.
  3. Calculate g(x−2)g(x-2): Calculate g(x−2)g(x-2) when x=4x=4.\newlineg(x)=5xg(x) = 5x, so g(x−2)=5(x−2)=5x−10g(x-2) = 5(x-2) = 5x - 10.\newlineNow, substitute xx with 44: g(4−2)=5(4−2)=5×2=10g(4-2) = 5(4-2) = 5\times2 = 10.
  4. Calculate h(x)h(x): Calculate h(x)h(x) using the values from Step 22 and Step 33.h(x)=2f(x−3)+2g(x−2)h(x) = 2f(x-3) + 2g(x-2). Substitute f(4−3)f(4-3) and g(4−2)g(4-2) into h(x)h(x): h(4)=2∗(−3)+2∗10h(4) = 2*(-3) + 2*10.
  5. Simplify to Find h(4)h(4): Simplify the expression to find h(4)h(4).h(4)=2×(−3)+2×10=−6+20=14h(4) = 2 \times (-3) + 2 \times 10 = -6 + 20 = 14.

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