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For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).

1 Answer

1 vote

Answer:


\displaystyle F(b + 3) = b^2 + 4b + 7

Explanation:

We are given the function:


\displaystlye F(x) = x^2 - 2x + 4

And we want to find F(b + 3).

We can substitute:


\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4

Expand:


\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4

Rearrange:


\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)

Combine like terms. Hence:


\displaystyle = b^2 +4b + 7

In conclusion:


\displaystyle F(b + 3) = b^2 + 4b + 7

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