If f(x) = x + 7 and g(x) = 1 / x - 13, whaf is the domain of (f°g)(x)?

Choice D) x can be anything but 13

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Explanation:

The domain of is the same as the domain of g(x)

The domain for g(x) is saying we can plug in any number we want as long as it's not 13. This is to avoid dividing by zero. The same domain applies for the composite function because

and we can see that we still need to kick out x = 13 from the domain to avoid the division by zero issue.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c