Question

Find the inverse function of f.
f(x)=4-5x^3

Answer 1

can you solve
\[-131=4-5\times x^3\] for \(x\)?

Answer 2

f^-1(x)=^3sqrt 4/5-1/5x

Answer 3

x=4-5y^3
solve for y

Answer 4

\[
x=4-5[f^{-1}(x)]^3
\]

Answer 5

im very confused

Answer 6

i will ask the question again
if it is not clear how to do it, then we need to do this one first
solve
\[-132=4-5x^3\]

Answer 7

yeah 5 of us are giving different approaches

Answer 8

oops i meant
\[-131=4-5x^3\] solve for \(x\) in 3 steps

Answer 9

I didn't tell you how to do it, I just gave you the answer.

Answer 10

and lets keep track of the steps when we do it

Answer 11

i need to know how to do it

Answer 12

Inverse functions are basically that function the opposite flow
for example if
F(x) = 2x +3
f'(x) = (y-3)/2

Answer 13

backing out of the crowded room

Answer 14

f^-1*

Answer 15

I still have calculus in ma head ._.

Answer 16

\[-131=4-5x^3\] subtract \(4\) from both sides, get
\[-135=-5x\] divide both sides by \(-5\)
\[-27=x^3\] take the cubed root of both sides
\[\sqrt[3]{27}=x\] or \[x=3\]

Answer 17

where did 131 come from?

Answer 18

now we can do the same thing to solve
\[x=4-5y^3\] but this time without numbers
subtract \(4\) from both sides
\[x-4=-5y^3\]
divide both sides by \(-5\)
\[\frac{x-4}{-5}=y^3\] take the cubed root of both sides
\[\sqrt[3]\frac{x-4}{-5}=y\] or
\[y=-\sqrt[3]{\frac{x-4}{5}}\]

Answer 19

i made up the \(-131\) because if you can do it with \(-131\) you can to it with \(x\) but if you cannot, then you cannot

Answer 20

Oh I get it

Answer 21

find the inverse of x/x+9

Answer 22

once again, how would you solve
\[7=\frac{x}{x+9}\]?

Answer 23

No idea

Answer 24

i would multiply by \(x+9\) on both sides first

Answer 25

\[7=\frac{x}{x+9}\\7(x+9)=x\]

Answer 26

whats next?

Answer 27

distribute

Answer 28

right
\[7x+7\times 9=x\] then what?

Answer 29

7x+63=x

Answer 30

after that i mean

Answer 31

idk

Answer 32

you want to get \(x\) on one side of the equal sign
at the moment you have \(7x\) on the left, and \(x\) on the right
subtract \(x\) from both sides

Answer 33

ok

Answer 34

what do you get?

Answer 35

idk

Answer 36

what is \(7x-x\)?

Answer 37

6x

Answer 38

ok good
and what is \(x-x\)?

Answer 39

0

Answer 40

right, so you have
\[6x+63=0\] now subtract \(63\) from both sides

Answer 41

x=10.5

Answer 42

ok good
now lets review the steps, because we are going to have to do them again, but without numbers
1) multiply both sides by \(x-9\)
2) distribute
3) subtract \(x\) from both sides
4) put everything without \(x\) on the other side
5) divide by the coefficient of \(x\)

Answer 43

now we solve
\[x=\frac{y}{y+9}\] for \(y\)
1) multiply both sides by \(y+9\) and get
\[x(y+9)=y\] 2) distribute \[xy+9x=y\]
3) subtract\(y\) from both sides
\[xy-y+9x=0\] 4) subtract \(9x\) from both sides
\[xy-y=-9x\]

Answer 44

now we have a step we did not do before
we have to factor out the \(y\) on the left, because we don't know what \(xy-y\) is unlike say \(7y-y\) which we know is \(6y\)
here you get
\[(x-1)y=-9x\]

Answer 45

last step is to divide, giving
\[y=\frac{-9x}{x-1}\]