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Determine the domain of the function $g(t)=\sqrt{3-t}$ and express it in interval notation.Solution:What can $t$ be? Any nonnegative real number. $3-t>0$$3>t \quad$ or $\quad t<3$Domain: $(-\infty, 3)$This is incorrect. What mistake was made?

$(-\infty, 3]$

Precalculus

Algebra

Chapter 1

Functions and Their Graphs

Section 1

Functions

Algebra Topics That are Reviewed at the Start of the Semester

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Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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in this problem, we are given the function G f t equals square root of three minus T. And asked to determine the domain of this function. We are also given to find the domain of the function as a solution that is three minus T greater than zero. And domain has given us NATO infant E come out three. So let's see how to find the domain of this function. We know the domain of a radical function. When you try to solve the domain for the radical function, we always take the inside part and ensure that it is greater than or equal to zero, So that we always take the square it for posture numbers and not for 92 numbers. So therefore this must be the inside part. Under this article, this must be rather than or equal to zero. So that's why we write on this as an inequality three minus together than or equal to zero. Now, let's try to solve the T four from this inequality. So it's a packed three from both sides. When you do that, we'll get NATO t Greater than or equal to -3. And we will solve 40 by dividing both sides by -1. When we do that we'll get t less than or equal to three. What is that? When you divide uh divide an inequality either by minus one or we multiply inequality by minus man. We will always start to change the inequality. So this means there is greater than or equal to or greater than oracle will become less than article group. So that's why we make this change over here. This is an important thing when solving the inequality. So finally this is the domain of them function Joppy so which can be returned in interval notation as negative infinity, comma three. We put this parenthesis for learning to infantry and we have to put a Squire record for the three so that this is always included. So this is an important uh, important thing in writing the Romanian interpretation. When you look at the domain, which is actually given in the solution, we don't see them, but we don't see the square bracket next to the three. So this, in fact, mr mistake.

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