Question

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

Answer 1

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

$g(x) = 6x$

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

$(g - f)(3) = 18 - (-9 + 4)$ 

$(g - f)(3) = 18 - (-5)$

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

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

Answer 2

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