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solve

3x^2-9x+5<0

The solution you posted above is by no means Q.E.D my friend, please rethink your solution, or at least your presentation of it.

f(x) = x/(x+1) , g(x) = x¹⁰, h(x) = x + 3.

Find: f o g o h

pronunciation: f of g of h.

f o g o h = f[x o x + 3]
              =f[x^2 + 3x]
              =x^2 + 3x(x^2 + 3x + 1)
              =X^4+3X^3+X^2+3X^3+9X^2+3X
              =X^4 + 6X^3 + 10X^2 + 3X.

Hey, i don't know if i did that right, kind of confused by what u meant by f(x)=x/(x+1). is d slash supposed to be there or not?

hmm, aight, i thought the slash was an error, that am only multiplyin because of the parentheses.

ok, i guess it's this way:
f o g o h = f[x o x + 3]
              =f[x^2 + 3x]
              =x^2 + 3x/ x^2 + 3x + 1
             
hmm, can't break it down any further, is that right or what?

Solve:



f(x) = (x-1) / (x²-1)
find f(1)

f(1)=(1-1)/ (1²- 1)
f(1) =0/0
f(1)=0

Solution:

a:
a²/a^1/2 =a^3/2
b/b^1/3 = b^2/3

multiplying the two, you get: a^3/2 .b^2/3


b:
81^-1/4 = 1/81^1/4 = 1/3

Given f(x) = sqrt(x) and g(x) = sqrt(4-x²)
Find the doman of (f+g)(x)

The solution you posted above is by no means Q.E.D my friend, please rethink your solution, or at least your presentation of it.
TempleID: The above statement insults my little mathematical acumen! I tried rethinking and resolvine and got the solution to the LHS as still x = 2.2638 or 0.73634 . If we substitute into the problem we have:

(x-2.2638)(x-0.73634)<0

N/D.  All terms in the question is reduced by 5
I stop there in order not to repear myselfe. Could you please profer solution or atleast an hint to the solution?

Thank you.

Given f(x) = x³ + 2

Find F^-1(x)

The inverse of the function is:

Cube root of (x-2).

How about that.

nice thread, i'm in

intergrate

2x^2 +5e^2x+ln7x

The question is not as complicated as it looks at first glance.

break the equation into 2 parts i.e

Part A is  2x^2  which integrates into 2(x^3)/3

Part B is 5e^2x+ln7x  i am assuming you mean 5e^(2x+ln 7x) because that is the only thing that makes the equation difficult to integrate.

we can write part B as 5e^2x (e^ln7x) now applying integration by parts which is u∫dv =uv - v∫du

let                             5e^2x = dv      and                 e^ln7x = u

it follows that if         u = e^ln 7x
then                       ln u = ln 7x             (Taking antilog of both sides)
                             du/u = dx/x             (Obtained by letting 7x = k. dk/dx = 7  & du/dk = u/k therefore  du/dx = dk.dk/dx )
 therefore              du    = 7 dx             ( u = 7x)
also to obtain v we integrate  5e^2x
therefore                   v  = 5/2 .e^2x

Part B becomes
           ∫5e^2x (e^ln7x) =  (e^ln7x) 5/2e^2x  - ∫ 5/2e^2x .7dx
which after integrating becomes               = (e^ln7x) 5/2e^2x  - (35/4) e^2x

Joining parts A & B together we obtain:  2(x^3)/3 + (e^ln7x) 5/2e^2x  - (35/4) e^2x  which is the solution.

i have tried solving this Nella and i seem to be getting an impossible situation
I don't know if iam the one wrong.
But this is how  i have tried to solve it.


sqrt(x-2) = sqrt(x+1) - 3
collecting like terms,
sqrt(x-2)- sqrt(x+1)= -3
((x-2) - (x+1))^1/2 = -3
Squaring both sides
(x-2) - (x+1) = 9
x-2-x-1= 9
This doesn't look good from here.
Guys correct my mistakes

derivative F(x) = -8x+2
F(6) of the derivative = -46 



Indicate which of the following functions doesn't have an inverse :

A(x) = 2x^3 +3

B(x) = 2\ x^2 + 1

C(x) = (x+2)\(3x-4)