Question

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

Answer 1

For this case we have the following functions:

$f (x) = 4 - x ^ 2\\g (x) = 6x$

The first thing we must do for this case is to subtract both functions.

We have then:

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

Substituting we have:

$(g - f) (x) = (6x) - (4 - x ^ 2)$

Rewriting we have:

$(g - f) (x) = x ^ 2 + 6x - 4$

Evaluating the obtained function for x = 3 we have:

$(g - f) (3) = (3) ^ 2 + 6 (3) - 4\\(g - f) (3) = 23$

Answer:

The value of the function evaluated at x = 3 is:

$(g - f) (3) = 23$

Answer 2

F(x) = -x² + 4
g(x) = 6x

(g - f)(3) = 6(3) - (-(3)² + 4)
(g - f)(3) = 18 - (-9 + 4)
(g - f)(3) = 18 - (-5)
(g - f)(3) = 18 + 5
(g - f)(3) = 23