Answer:
[tex]x = 2~\text{and} ~x = -3[/tex]
Step-by-step explanation:
[tex]~~~~~~f(x) = g(x)\\\\\implies -x +4 =x^2 -2\\\\\implies x^2 -2+x -4=0\\\\\implies x^2 +x -6 = 0\\\\\implies x^2 +3x -2x -6 =0\\\\\implies x(x+3) - 2(x+3) = 0\\\\\implies (x-2)(x+3) = 0\\\\\implies x = 2,~ x = -3[/tex]
Answer:
x = -3 and x = 2
Step-by-step explanation:
Plotting the graphs :
f(x)
⇒ Find two points (preferably the x and y intercepts)
⇒ 0 = -x + 4
⇒ x = 4
⇒ Point 1 : (4, 0)
⇒ f(x) = 0 + 4
⇒ f(x) = 4
⇒ Point 2 : (0, 4)
g(x)
⇒ g(x) = 0 - 2
⇒ g(x) = -2
⇒ Point 1 : (0, -2)
⇒ g(x) = 2² - 2
⇒ g(x) = 2
⇒ Point 2 : (2, 2)
* Graph with both functions is attached below *
=============================================================
Finding the solutions :
⇒ Equate f(x) and g(x)
⇒ -x + 4 = x² - 2
⇒ x² + x - 6 = 0
⇒ x² + 3x - 2x - 6 = 0
⇒ (x + 3)(x - 2) = 0
⇒ x = -3 and x = 2
