Question

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

Answer 1

`\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`