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

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

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Full solution

Q. Given that f(x)=x+4,g(x)=2x f(x)=x+4, \quad g(x)=2 x and h(x)=−3f(x+2)+2g(x) h(x)=-3 f(x+2)+2 g(x) , then what is the value of h(2) h(2) ?\newlineAnswer:
  1. Find f(2)f(2): First, we need to find the value of f(x)f(x) when xx is replaced by 22.
    f(x)=x+4f(x) = x + 4
    f(2)=2+4f(2) = 2 + 4
    f(2)=6f(2) = 6
  2. Find g(2)g(2): Next, we need to find the value of g(x)g(x) when xx is replaced by 22.
    g(x)=2xg(x) = 2x
    g(2)=2×2g(2) = 2 \times 2
    g(2)=4g(2) = 4
  3. Find f(x+2)f(x+2): Now, we need to find the value of f(x+2)f(x+2). Since we already know f(x)f(x), we can replace xx with (x+2)(x+2) in the function f(x)f(x).
    f(x+2)=(x+2)+4f(x+2) = (x+2) + 4
    f(2+2)=(2+2)+4f(2+2) = (2+2) + 4
    f(4)=4+4f(4) = 4 + 4
    f(4)=8f(4) = 8
  4. Find h(2)h(2): With the values of f(4)f(4) and g(2)g(2), we can now find h(x)h(x) when xx is replaced by 22.
    h(x)=−3f(x+2)+2g(x)h(x) = -3f(x+2) + 2g(x)
    h(2)=−3f(2+2)+2g(2)h(2) = -3f(2+2) + 2g(2)
    h(2)=−3f(4)+2g(2)h(2) = -3f(4) + 2g(2)
    h(2)=−3×8+2×4h(2) = -3 \times 8 + 2 \times 4
    f(4)f(4)00
    f(4)f(4)11

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