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Interval Notation?

Let f(x) = sqroot(x-3) and g(x) = x (squared) + 1. Compute (g of f)(x), state its domain in interval notation.

It’s ok if you don’t do the problem, I really just need someone to explain in simple terms how interval notation works, and if you could, how I’d relate it to the domain.

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To find g(f(x)), replace x in g(x) with f(x):

g(f(x)) = f(x)^2 + 1

= [sqrt(x – 3)]^2 + 1

= x – 3 + 1

= x + 2.

The domain of sqrt(x – 3) is values of x for which x – 3 >= 0, as sqrt(u) is not defined for negative u.

The domain is therefore x >= 3, and you write this as

[3, infty).

A square bracket shows that the number (3 in this case) is included in the range. A round bracket shows that the number (infinity in this case) is excluded. Infinity is always excluded, as it is not a number in the true sense.


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