Question

Evaluate (f − g)(2) for f(x) = 2x2 − 18 and g(x) = –3x − 7.

Answer 1

For this case we have the following functions:

$f (x) = 2x ^ 2-18\\g (x) = - 3x-7$

We must find:

$(f-g) (2)$

By definition, we have to:

$(f-g) (x) = f (x) -g (x)$

So:

$(f-g) (x) = 2x ^ 2-18 - (- 3x-7)\\(f-g) (x) = 2x ^ 2-18 + 3x + 7\\(f-g) (x) = 2x ^ 2 + 3x-11$

Then, we evaluate in x = 2:

$(f-g) (2) = 2 (2) ^ 2 + 3 (2) -11\\(f-g) (2) = 2 (4) + 6-11\\(f-g) (2) = 8 + 6-11\\(f-g) (2) = 8 + 6-11\\(f-g) (2) = 3$

ANswer:

$(f-g) (2) = 3$