Answer:
See attachment
Step-by-step explanation:
A function is given to us and we need to tell which graph represents the given function. The function given to us is,
Let's find out at which points do the graph Intersects x axis / finding the roots. For that substitute f(x) = 0 , we have ,
Equate each factor by 0 ,
Therefore the graph will intersect x axis at x is equal to -1 and x is equal to -3 .
On looking at the given graphs in the options the second graph intersects x axis at -1 and -3 .
<u>Hence</u><u> </u><u>the </u><u>second</u><u> </u><u>option</u><u> </u><u>is </u><u>correct</u><u> </u><u>.</u><u> </u>
{ See attachment }
The value of x that will satisfy the equation is x=-1.
We have given that,

We have to solve the above inequality
<h3>What is inequality?</h3>
Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.
Find the positive and negative intervals

Solve the inequality for each interval


Therefore we get,

To learn more about inequality visit:
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Here we are to find the values of x in which the function
f (x) = csc 5x is discontinuous. What this usually means is to find when the
value approaches infinity.
We know from trigonometric identities that csc is the
equivalent to 1 / sin, therefore the function in terms of sin is:
f(x) = 1 / sin 5x
We can see that the function becomes discontinuous when sin
5x = 0, that is a value divided by 0 is discontinuous or approaches infinity.
sin 5x is equal to zero when:
5x = 0 or π
So given k as an arbitrary integer
5x = k π
So k can be: k = 0, 1, 2
x = k π/ 5
Use the Pythagorean theorem to find X
A² + B² = C²
X² + 4² = 5²
X² = 5² - 4²
X² = 25 - 16
X² = 9
.: X = 3