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Given that f(x)=5x,quad g(x)=x-2 and h(x)=-2f(x+3)-3g(x), then what is the value of h(6) ? Answer:

Given that f(x)=5x,g(x)=x−2 f(x)=5 x, \quad g(x)=x-2 and h(x)=−2f(x+3)−3g(x) h(x)=-2 f(x+3)-3 g(x) , then what is the value of h(6) h(6) ?\newlineAnswer:

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Q. Given that f(x)=5x,g(x)=x−2 f(x)=5 x, \quad g(x)=x-2 and h(x)=−2f(x+3)−3g(x) h(x)=-2 f(x+3)-3 g(x) , then what is the value of h(6) h(6) ?\newlineAnswer:
  1. Define functions: Define the functions f(x)f(x), g(x)g(x), and h(x)h(x) as given.f(x)=5xf(x) = 5x, g(x)=x−2g(x) = x - 2, and h(x)=−2f(x+3)−3g(x)h(x) = -2f(x + 3) - 3g(x).
  2. Calculate f(9)f(9): Calculate f(6+3)f(6 + 3) since we need to evaluate h(6)h(6) and h(x)h(x) involves f(x+3)f(x + 3).\newlinef(6+3)=f(9)=5×9=45f(6 + 3) = f(9) = 5 \times 9 = 45.
  3. Calculate g(6)g(6): Calculate g(6)g(6) since we need to evaluate h(6)h(6) and h(x)h(x) involves g(x)g(x).\newlineg(6)=6−2=4g(6) = 6 - 2 = 4.
  4. Substitute into h(x)h(x): Substitute f(9)f(9) and g(6)g(6) into the equation for h(x)h(x) to find h(6)h(6).\newlineh(6)=−2×f(9)−3×g(6)=−2×45−3×4h(6) = -2 \times f(9) - 3 \times g(6) = -2 \times 45 - 3 \times 4.
  5. Perform arithmetic operations: Perform the arithmetic operations to find the value of h(6)h(6).h(6)=−2×45−3×4=−90−12=−102h(6) = -2 \times 45 - 3 \times 4 = -90 - 12 = -102.

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