Question

y=2x^3+3x+4
find the inverse

Answer 1

all you'd do is swap about the variables like so \(\bf y=2x^3+3x+4\qquad inverse\implies x=2y^3+3y+4\)

and solve for "y"

Answer 2

@majdishokri Are you still stuck?

Answer 3

yes

Answer 4

Do you know how to complete the square?

Answer 5

not good

Answer 6

First divide by \(2\) because you want \(y^2\) on its own: \[
\frac x2=y^2+\frac 32y+2
\]

Answer 7

but why we want to complete the square for this question

Answer 8

Now you identify the middle coefficient is \(3/2\)

Answer 9

So that we can solve for \(y\).
You can also use the quadratic equation if you really want to.

Answer 10

@wio, there's a \(y^3\) term

Answer 11

y ^3 not y^2

Answer 12

???????????????????????????????????????????????????

Answer 13

Okay fine, first solve for \(y\) \[
y = \frac{x-4-2y^3}{3}
\]And expand it: \[

y = \frac{x-4-2y^3}{3}=\frac{x-4-2\left(\frac{x-4-2y^3}{3}\right)^3}{3}
\]

Answer 14

What class is this, by the way?

Answer 15

calculus 101

Answer 16

Do you know how to differentiate?

Answer 17

how u do that in the first step

Answer 18

Maybe they want you to do implicit differentiation.

Answer 19

this is a very complex question

Answer 20

What have you learned recently?

Answer 21

\[x=2y ^{3}+3y +4\]
\[x-4=y(2y ^{2}+3)\]
\[x-4\frac{ }{ ? }\]

Answer 22

What concepts have you learned in your class recently?

Answer 23

log

Answer 24

????????

Answer 25

log? Like logarithmic differentiation?

Answer 26

yes