Question

If h(x)=x+sqrt(x)
find
f^-1(6)

Answer 1

\[h(x) = x+\sqrt{x}\]

and

\[f^{-1} (6)\]

right?

Answer 2

Correct :)

Answer 3

\[f^{-1} = inverse function \]

Answer 4

This is asking you to take the inverse of the function then evaluate it do you know how to do this?

Answer 5

So first we set
y=x+sqrt(x)
and then solve that for x?

Answer 6

you need to switch the x and y's in the original function and solve for y

Answer 7

Ah ok, let me see.

Answer 8

so we have
x=y+ sqrt(y)

Answer 9

then solve for y

Answer 10

Then you can evaluate this for say f^-1(6)

Answer 11

Would a good first step be
(x-y)^2 = y
and then of course continue solving

Answer 12

\[x^2=(1+2x+y)y\]lala still simplifying xD

Answer 13

well

Answer 14

your "simplification" looks correct :) BUT
the "y" will be pervasive on either side though

Answer 15

now lemme hmm graph the original fuhction, one sec

Answer 16

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4K3NxcnQoeCkiLCJjb2xvciI6IiNFMzBEMEQifSx7InR5cGUiOjAsImVxIjoieC1zcXJ0KHgpIiwiY29sb3IiOiIjMTkxRkNGIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTQuNjQ5OTk5OTk5OTk5OTk5IiwiMTEuNTk5OTk5OTk5OTk5OTk4IiwiLTIuMjk5OTk5OTk5OTk5OTk5NCIsIjcuNyJdfV0-


notice
if you give a "vertical line test", it won't pass it, meaning, is not a function, just a relation
and only one-to-one "functions" have an "inverse function"

and one-to-one functions, need to pass the vertical and horizontal line tests
this one fails both

which as far as I can tell, is why is ending up in a deadend

Answer 17

mm well I have an answer that I SHOULD be able to arrive too. There's just a lot of algebra I guess xD

Answer 18

right... was thinking the same... it should be decouplable
just lengthy

Answer 19

\[\frac{ x^2 }{ 1+2x+y}=y\]

Answer 20

Maybe multiply the left side by y?

Answer 21

hmmm

Answer 22

or add y to the left side..might work

Answer 23

ooh you know what
we can just do h(x) = x+sqrt(x) = 6 and solve that
and then figure it out from there..no?

Answer 24

Because we know the rule for example;
f(6)=17 then f^-1(17)=6

Answer 25

\[x+ \sqrt x=6\]\[x=3\]
h(3)=6
\[f^{-1}(6)=3\]

Answer 26

*x=4
so f inverse(6)=4