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20 November, 00:45

Based on the graph below, what is the solution to the equation f (x) = g (x) ?

graph of function f of x equals negative x plus 2.5 and graph of function g of x equals x squared plus 2 multiplied by x minus 8

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  1. 20 November, 01:00
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    The wording of the second function may be interpreted in several differente ways. These are some:

    g (x) = (x^2 + 2) (x-8)

    g (x) = x^2 + 2 (x-8)

    g (x) x^2 + 2x - 8

    I will work with the last one, so my system of equation is:

    f (x) = - x + 2.5

    g (x) = x^2 + 2x - 8

    f (x) = g (x) ⇒ - x + 2.5 = x^2 + 2x - 8

    x^2 + 3x - 8 - x - 2.5 = 0

    x^2 + 3x - 10.5 = 0

    Use the quadratic formula to solve for x:

    x = [ - 3 + / - √ (3^2) - 4 (1) (-10.5) ]/2

    x = - 5.07 and x = 2.07
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