Question

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

Answer 1

f(x) = 4 - x² Df: x∈R

g(x) = 6x Dg: x∈R

Df = Dg therefore (g - f)(x) = g(x) - f(x)

(g - f)(3) = g(3) - f(3)

subtitute the value of x to equations:

g(3) = 6 · 3 = 18
f(3) = 4 - 3² = 4 - 9 = -5

(g - f)(3) = 18 - (-5) = 18 + 5 = 23

Answer 2

`f(x) = -x^2 + 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`