Answer: Choice D) 7x+2; all real numbers
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Work Shown:
f(x) + g(x) = [ f(x) ] + [ g(x) ]
f(x) + g(x) = [ 4x-5 ] + [ 3x+7 ]
f(x) + g(x) = 4x-5 + 3x+7
f(x) + g(x) = (4x+3x) + (-5+7)
f(x) + g(x) = 7x+2
The domain of y = 7x+2 is the set of all real numbers. There are no restrictions to worry about such as dividing by zero or taking the square root of a negative number. We can plug in any real number we want for x to get some output for y. This is one of the many properties of linear equations.