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f(x)=x2+1f(x) = x^2 + 1\newlineg(x)=5xg(x) = 5 – x \newlineFind (f+g)(x)=(f + g)(x) =

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Q. f(x)=x2+1f(x) = x^2 + 1\newlineg(x)=5xg(x) = 5 – x \newlineFind (f+g)(x)=(f + g)(x) =
  1. Write Expressions: To find the sum of the functions f(x)f(x) and g(x)g(x), we need to add the two functions together. The function f(x)f(x) is given as f(x)=x2+1f(x) = x^2 + 1, and the function g(x)g(x) is given as g(x)=5xg(x) = 5 - x. We will add these two functions to find (f+g)(x)(f + g)(x).
  2. Add Functions: We write down the expressions for f(x)f(x) and g(x)g(x) next to each other to prepare for addition: f(x)=x2+1f(x) = x^2 + 1 and g(x)=5xg(x) = 5 - x.
  3. Combine Like Terms: Now we add the two functions together: (f+g)(x)=f(x)+g(x)=(x2+1)+(5x)(f + g)(x) = f(x) + g(x) = (x^2 + 1) + (5 - x).
  4. Simplify Constants: We combine like terms in the expression: (f+g)(x)=x2+1+5x(f + g)(x) = x^2 + 1 + 5 - x.
  5. Simplify Constants: We combine like terms in the expression: (f+g)(x)=x2+1+5x(f + g)(x) = x^2 + 1 + 5 - x.Simplify the constant terms: (f+g)(x)=x2x+6(f + g)(x) = x^2 - x + 6.

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