What kind of number is 0.87 rational or irrational

A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

$f(g(x))= f(\frac{2x+1}{x} )$

$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

$g(\frac{1}{x-2} )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

B.

For the Composition function $f(g(x)) = f(\frac{2x+1}{x} )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g(\frac{1}{x-2} )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

8 0

3 years ago

2(x-3)=7x-31 3x-2 (x+5)=-3+18 Please show your work

vredina [299]

2(x-3)=7x-31
2x-6=7x-31
-7x -7x
----------------
-5x-6=-31
+6 +6
--------------
-5x=-25
Divide by -5
x=5

3x-2(x+5)=-3+18
15
3x-2(x+5)=15
3x-2x-10=15
x-10=15
+10 +10
--------------
x=25

3 0

3 years ago

Use the law of cosines to find the length of a

borishaifa [10]

Answer:

Step-by-step explanation:

You don't need the Law of Cosines, the Law of sines if what you need. You can't use the Law of Cosines because in order to find side a, you would need the length of side c and you don't have it. Using the Law of Sines is appropriate, knowing that angle B = 55:

$\frac{sin55}{175}=\frac{sin42}{a}$ and solving for a:

$a=\frac{175sin42}{sin55}$ so

a = 143.0

4 0

2 years ago

Graph y=4/7x−2 . Use the line tool and select two points on the line.

Lynna [10]

Answer:

Given equation of the line,

$y=\frac{4}{7}x-2$

If x = 0,

$y=\frac{4}{7}(0) - 2=0-2=-2$

Thus, the line intercepts y-axis at (0,-2)

If y = 0,

$0=\frac{4}{7}x-2\implies 2=\frac{4}{7}x\implies x=\frac{14}{4}=3.5$

Thus, the line intercepts x-axis at (3.5,0)

By joining these two points in the graph,

We will get the graph of the given line ( shown below )

4 0

3 years ago

My question : here is related to Algebra 1 HELP

Ilia_Sergeevich [38]

Answer:

The sun is about 390 times farther than earth is from the moon

Step-by-step explanation:

It's kind of hard to understand the question but it's essentially asking how many times farther earth is from the sun than earth is from the Moon. Or basically measure the distance from the earth to the moon. Then show how much bigger the distance from the Earth to the Sun is by comparing it from the earth to the moon. To do this you divide the distance of moon by the distance of the sun to get how many times you could you could fit the distance between the Earth and The Moon from the Earth to the Sun.

4 0

2 years ago

What kind of number is 0.87￼ rational or irrational

What kind of number is 0.87 rational or irrational