Question

For f(x) = 2x + 1 and g(x) = x^2 - 7, find (f-g)(x)

Answer 1

`→(f - g)(x) \\ = f(x) - g(x) \\ = (2x + 1) - ( {x}^(2) - 7) \\ = 2x + 1 - {x}^(2) + 7 \\ = \boxed{ - {x}^(2) + 2x + 8}✓`

• -x²+2x+8 is the right answer.

Answer 2

`\displaystyle (f - g)(x) = -x^2 + 2x + 8`

Explanation:

We are given the two functions:

`\displaystyle f(x) = 2x + 1 \text{ and } g(x) = x^2 - 7`

And we want to find:

`\displaystyle (f- g)(x)`

Recall that:

`\displaystyle (f - g)(x) = f(x) - g(x)`

Substitute and simplify:

`\displaystyle \begin{aligned}(f-g)(x) &= f(x) - g(x) \\ \\ &= (2x + 1) - (x^2 - 7) \\ \\ &= (2x +1 )+ (-x^2 + 7) \\ \\ &= -x^2 +2x + 8\end{aligned}`

In conclusion:

`\displaystyle (f - g)(x) = -x^2 + 2x + 8`