Question 354852
Solve the equation/ Check for extraneous solutions.
1.x^(1/2)+5=4
x^(1/2) = -1
x = 1
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2.3(to the squar root of)2x+4=12
3*sqrt(2x+4) = 12
sqrt(2x+4) = 4
2x+4 = 16
2x = 12
x = 6
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3.( cubed root of the Nth root or what ever) inside is x+40=-5
(x+40)^(1/3) = -5
x+40 = -125
x = -165
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4.x-4= square root of 2x 
x-4 = sqrt(2x)
(x-4)^2 = 2x
x^2 -8x + 16 = 2x
x^2 - 10x + 16 = 0
(x-2)(x-8) = 0
x = 2 or x = 8
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Checking in the original equation you get
x = 2 but x cannot be 8
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a) perform the indicated operation 
b) State the domain of the result
F(x)=3x and g(x)= x-5 
5.F(x)+ g(x) = 3x+x-5 = 4x-5
Domain: All Real Numbers
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6.F(x)/G(x) = 3x/(x-5)
Domain: All Real Numbers except x = 5
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7.f(x)*g(x) = (3x)(x-5) = 3x^2-15x
Domain: All Real Numbers
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8.f(g(x)) = f(x-5) = 3(x-5) = 3x-15
Domain: All Real Numbers
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Cheers,
Stan H.