Choice B) x = 3; 7
This is the same as saying x = 3 and x = 7.
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Work Shown:
Plug x = 3 into f(x)
f(x) = (1/2)*|x-3| + 3
f(3) = (1/2)*|3-3| + 3
f(3) = 0.5*|0| + 3
f(3) = 0.5*0 + 3
f(3) = 0 + 3
f(3) = 3
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Plug x = 5 into f(x)
f(x) = (1/2)*|x-3| + 3
f(5) = (1/2)*|5-3| + 3
f(5) = 0.5*|2| + 3
f(5) = 0.5*2 + 3
f(5) = 1 + 3
f(5) = 4
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Plug x = 7 into f(x)
f(x) = (1/2)*|x-3| + 3
f(7) = (1/2)*|7-3| + 3
f(7) = 0.5*|4| + 3
f(7) = 0.5*4 + 3
f(7) = 2 + 3
f(7) = 5
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Plug x = 3 into g(x)
g(x) = sqrt(x-3) + 3
g(3) = sqrt(3-3) + 3
g(3) = sqrt(0) + 3
g(3) = 0 + 3
g(3) = 3
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Plug x = 5 into g(x)
g(x) = sqrt(x-3) + 3
g(5) = sqrt(5-3) + 3
g(5) = sqrt(2) + 3
g(5) = 1.414214 + 3
g(5) = 4.414214 ..... which is approximate
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Plug x = 7 into g(x)
g(x) = sqrt(x-3) + 3
g(7) = sqrt(7-3) + 3
g(7) = sqrt(4) + 3
g(7) = 2 + 3
g(7) = 5
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To summarize everything, refer to the table below.
The rows highlighted in yellow refer to when f(x) = g(x)
This happens twice when x = 3 and x = 7
If x = 3, then f(x) = g(x) = 3
If x = 7, then f(x) = g(x) = 5
Therefore, x = 3 and x = 7 are two solutions to f(x) = g(x)
