Question

Graph the functions on the same coordinate plane.

f(x)=−x+4

g(x)=x2−2

What are the solutions to the equation f(x)=g(x) ?

Select each correct answer.


3

−3

−2

2

0

Answer 1

x = -3 and x = 2

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 *

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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

Answer 2

`x = 2~\text{and} ~x = -3`

Explanation:

`~~~~~~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`