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Two functions are shown in the table below.

Function - 1,2,3,4,5,6

f(x) = −x2 + 4x + 12
g(x) = x + 8
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).

x = 6
x = 3
x = 5
x = 4

Respuesta :

MrRoyal

Answer:

[tex](d)\ x = 4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = -x^2 + 4x + 12[/tex]

[tex]g(x) = x + 8[/tex]

Required

Find x such that: [tex]f(x) = g(x)[/tex]

This gives:

[tex]-x^2 + 4x + 12 = x+8[/tex]

Collect like terms

[tex]-x^2 + 4x -x + 12 -8=0[/tex]

[tex]-x^2 + 3x +4 =0[/tex]

Expand

[tex]-x^2 + 4x - x+4 =0[/tex]

Factorize

[tex]x(x - 4) - 1(x-4) = 0[/tex]

Factor out x - 1

[tex](x- 1)(x - 4)=0[/tex]

Solve:

[tex]x =1\ or\ x = 4[/tex]

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