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What is the range of the function #x + sqrt( x-1 )#?

Answer 1

Ethan Adkins

Range of function: 1 ≤ x

In order to determine the range of a function, you look at the complex part of that function, in this case: #sqrt(x-1)#

It is always the most complicated portion of a function that limits it, so you have to start here.

We know for a fact that any square root must always be equal to or greater than zero. That is, it cannot be negative.

0 ≤ #sqrt(x-1)# 0 ≤ #x-1# 1 ≤ x

From the above, we can infer that the square root of x from the given function must always be greater than or equal to 1. If x were to be less than 1, this would not be possible.

This means that the function has a lower limit of 1 and no upper limits because you can now insert any value of x that is greater than or equal to 1.

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Answer 2

Avery Alexander

The range of the function (x + \sqrt{x-1}) is ([1, \infty)).

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Answer 3

Eva Adamson

The range of the function ( f(x) = x + \sqrt{x - 1} ) is ([1, \infty)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.