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Artist 52 [7]
2 years ago
7

F(x)=2x^2-x-6 g(x)=4-x (f+g)(x)

Mathematics
1 answer:
Semenov [28]2 years ago
8 0

\large  \boxed{(f + g)(x) = f(x) + g(x)}

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

\large{ \begin{cases} f(x) = 2 {x}^{2}   -  x - 6 \\ g(x) =  4 - x \end{cases}}  \\  \large{f(x) + g(x) = (2 {x}^{2}  - x - 6) + (4 - x)} \\  \large{f(x) + g(x) = 2 {x}^{2}  - x - 6 + 4 - x}

Évaluate/Combine like terms.

\large{f(x)  + g(x) = 2 {x}^{2}  - 2x - 2}

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

\large{(f + g)(x) = 2 {x}^{2}  -2x -2}

<u>Alternative</u>

\large{(f + g)(x) = 2({x}^{2}  -x - 1)}

<u>Answer</u>

  • (f+g)(x) = 2x²-2x-2
  • (f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!

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