1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ivolga24 [154]
3 years ago
6

Show that (f o g)(x) = (g o f)(x) = x

Mathematics
1 answer:
cluponka [151]3 years ago
6 0

Answer:

- \frac{2[1 - x]}{3}  = g[f(x)] \\  \\  \frac{3x}{2 - x}  = f[g(x)]

Step-by-step explanation:

They are not.

For the <em>g[f(x)]</em> function, you substitute ³/ₓ ₋ ₁ from the <em>f</em><em>(</em><em>x</em><em>)</em><em> </em>function in for <em>x</em><em> </em>in the <em>g</em><em>(</em><em>x</em><em>)</em><em> </em>function to get this:

\frac{2}{ \frac{3}{x - 1}}

Then, you bring <em>x</em><em> </em><em>-</em><em> </em><em>1</em><em> </em>to the top while changing the expression to its conjugate [same expressions with opposite symbols]:

- \frac{2[1 - x]}{3}

You could also do this [attaching another negative would make that positive].

For the <em>f[g(x)]</em> function, ²/ₓ from the <em>g(x)</em> function for <em>x</em><em> </em>in the <em>f(x)</em> function to get this:

\frac{3}{ \frac{2}{x} - 1}

Now, if you look closely, ²/ₓ is written as 2x⁻¹, and according to the Negative Exponential Rule, you bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM NEGATIVE TO POSITIVE:

\frac{3x}{2 - x}

When this happens, <em>x</em><em> </em>leaves the <em>two</em> and gets attached to the <em>three</em><em>,</em><em> </em>and 1 gets an <em>x</em><em> </em>attached to it.

I am joyous to assist you anytime.

You might be interested in
Find the domain of ( (a+b/b) − (a/a+b))÷( (a+b/a) − (b/a+b) )
Alexandra [31]

Answer:

Hence the domain is given as,b is such that b is a member of all real numbers,except b=0,a=0, a=-b

Step-by-step explanation:

The domain refers to values for which the expression is defined.

This implies that, the denominators are not equal to zero.

(\frac{a + b}{b} -  \frac{a}{a + b}) \div ( \frac{a + b}{a} -  \frac{b}{a + b})

(\frac{(a + b)(a + b)-ab}{b(a + b)})\div(\frac{(a + b)(a + b)-ab}{a(a + b)})

\frac{(a + b)(a + b)-ab}{b(a + b)} \times\frac{a(a + b)}{(a + b)(a + b)-ab}

\implies \frac{a}{b}

Hence the domain is given as,b is such that b is a member of all real numbers,except b=0,a=0, and a=-b

7 0
3 years ago
Read 2 more answers
Use the graph to find the x-intercept for the equation ý +2 Graph: Y + 2 = 2(x+3)
alex41 [277]

Answer:

(-2, 0)

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Alexis Brian and Carli collect graphic novels, Brian has 5 more graphic novels then Alexis and Carli has twice as many as Alexis
kkurt [141]
According to Google, a Variable is <span>any factor, trait, or condition that can exist in differing amounts or types. If you type in variable in the Google search bar, it will give you the definition in a little box at the very top of the page :).
</span>
4 0
3 years ago
Can anyone do these two<br> a)√3(√3-1)<br> b)√5(√10+√2)
gogolik [260]
A 1.267949192
b 10.23334547
7 0
3 years ago
Please help so I can pass
lora16 [44]
Your answer would be F.
4 0
3 years ago
Other questions:
  • What is the least common denominator that can be used to x+1 over 8x^2 add 2x-3 over 12x
    7·1 answer
  • I NEED HELP IN THIS QUESTION PLEASE
    6·2 answers
  • If f(x)= x^2 -2 and g(x)=x-3, what is (f o g)(X)?
    7·1 answer
  • Evaluate the expression 11!/7!
    8·2 answers
  • What is the value of the expression below?<br> (V9)2 +10
    10·2 answers
  • you have $220 in your savings account. you take #35 from your account each week for four weeks? How much is left in your account
    9·1 answer
  • If a letter is chosen at random from the word MATHEMATICS, what is the probability of choosing a T? A. 1/11 B. 2/11 C. 4/11 D. 5
    15·1 answer
  • In the diagram below, the red angle $(\angle YAK)$ and the blue angle $(\angle OAT)$ are both right angles. If $\angle YAO=23^\c
    5·2 answers
  • Please help ill give brainleist answer
    5·1 answer
  • A shape is rotated counterclockwise 110 degrees about the origin. What is another way to describe the rotation?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!