Question

find the inverse of f(x)=3 squareroot of x+3

Answer 1

using () to indicate what is under the radical for clarity ...

3 sqrt(x+3) i assume?

Answer 2

Yes!

Answer 3

y = 3 sqrt(x+3) ; solve for x really .... divide out the 3

y/3 = sqrt(x+3) ; ^2 the dies to get rid of the sqrt

(y/3)^2 = x+3 ; now -3 to get x all alone

(y/3)^2 - 3 = x ; and that you inverse

Answer 4

f-1(x) = (x/3)^2-3

Answer 5

that almost the inverse; we have to restrict it to match up tho

Answer 6

I am writing all of this down to see if I understand

Answer 7

(y/3)^2 - 3 produces two values for every input; which makes it not one to one material

Answer 8

we have to restrict it to y>=0 by convention

Answer 9

Wow. I am going over the problem real quick

Answer 10

y>=-3 maybe better :)

Answer 11

\[f(x)=\sqrt[3]{x+3}\]

Answer 12

\[f^{-1}(x)=x^3-3\]

Answer 13

no restrictions need apply

Answer 14

wow!! Ok, still looking just to make sure I understand

Answer 15

there is debate over whether the inverse is properly a function of y as opposed to x

Answer 16

i am assuming it is
\[f(x)=\sqrt[3]{x+3}\] not
\[f(x)=3\sqrt{x+3}\]

Answer 17

y = f(x) then its inverse is f-1(y) = x or some such

Answer 18

\[f(x)=\sqrt[3]{x+3}\] has domain all real number and range as well. there is no restriction unless you put one on it for some other reason, like say x is a length and has to be positive

Answer 19

So is f-1 (x)=x3-3?

Answer 20

Is this the answer?

Answer 21

it is
\[f^{-1}(x)=x^3-3\] with no restriction on domain or range

Answer 22

your original function f says
add 3
take the cube root

your inverse will then say
cube
subtract 3

Answer 23

Ok, thank you! Ya'll are so smart! Can someone help me with this one?

Answer 24

opposite operations in reverse order

Answer 25

i am assuming it is CUBE ROOT not 3 times SQUARE ROOT

Answer 26

Find the equation of the line in general form (5,-4) (-4,3) we know up until the slope which we get -7/9 but then what numbers do you input for the formula?

Answer 27

sensei is right if it is the second one.

Answer 28

in any case; the inverse is when you rewrite to problem to solve for the other variable

Answer 29

you ccan use either coordinate for theh formula as long as you put in y, m and x and leave b as a variable to be firgured out

Answer 30

P(x,y); Px, Py

y = mx -mPx +Py

Answer 31

use the almighty point slope formula
\[y-y_1=m(x-x_1)\] with
\[x_1=5, y_1=-4, m=-\frac{7}{9}\]

Answer 32

but standard form is is ax+by where slope = -a/b

Answer 33

y=mx+b
3=(-7/9)-4+b
3=28/9+b
solve for b...

Answer 34

standard form for me is
\[y=mx+b\] but i am surely wrong

Answer 35

i like slope intersect form...

Answer 36

7x +9y = n; plug in a point to calibrate for n

Answer 37

satellite, thats slope intersect... and btw you got my calc problem wrong ;)

Answer 38

whatever you are in to. you now have 3 essentially the same way of doing it. good luck

Answer 39

did not!

Answer 40

did too

Answer 41

really?

where was the mistake?

Answer 42

(5,-4)

7(4) +9(-4) = n

28 -36 = n

-8 = n

7x +9y = -8

Answer 43

you divided by two somewhere...

Answer 44

i am fairly sure the volume was
\[V(x)=x(7-2x)(10-2x)\] eys?

Answer 45

your answer gave me 1.3blah blah whereas the real answer is 2.7blahblah

Answer 46

you got the equations right, you solved for 0 wrong lol

Answer 47

really?

Answer 48

Wow! U guys r too smart for me to even figure out why you are arguing

Answer 49

\[V(x)=4 x^3-34 x^2+70 x\] yes?

Answer 50

\[V'(x)=12x^2-64x+70\] for sure

Answer 51

Someone else said that 7x+9y=-1

Answer 52

now i set = 0 and solve and get
oh oops

Answer 53

But someone here said it is -8

Answer 54

lol see you got it wrong :P