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The solution set of the inequality x ≥ - 4 using set builder notation and interval notation is {x | x ∈ Z, - 4 ≤ x ≤ ∞ } and [ - 4, ∞ ) respectively.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.

Interval Notation: A set of real numbers known as an interval contains all real numbers that fall inside any two of the set's numbers.

Consider the inequality,

x ≥ - 4

In the number line, the value of x is equal to and greater than - 4 increasing to infinity.

Therefore,

The solution set using the set builder notation is:

{x | x ∈ Z, - 4 ≤ x ≤ ∞ }

The solution set of the inequality using the interval notation is:

[ - 4, ∞ )

Learn more about set builder notation here:

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1 year ago

F(x) = x ^ 2 . What is g(x) ?

Bond [772]

Given:

The function is:

$f(x)=x^2$

The graphs of functions $f(x)$ and $g(x)$ .

To find:

The function $g(x)$ .

Solution:

We have,

$f(x)=x^2$

The function $f(x)$ is vertically compresses to get the graph of the function $g(x)$ . So, the function $g(x)$ is:

$g(x)=kf(x)$

$g(x)=kx^2$ ...(i)

From the given graph it is clear that the graph of the function $g(x)$ passes through the point (3,3). So, putting $x=3$ and $g(x)=3$ in the above function, we get