Question

If f(x)=x^5+x^3+x, what is the inverse of f(x)? I am stuck on the fact that there are three x's on the right side and when I try to factor I can't factor anything but one y out. (I'm using x-y substitution method) Any hints would be appreciated thanks.

Answer 1

may i knw why do you want to find the inverse ?

Answer 2

It is extra practice I'm doing because I want to review some pre-cal stuff before calculus.

Answer 3

i don't see any easy way to find the inverse.. could you provide more context of the problem and maybe post the actual complete question if psble

Answer 4

Did you come up this question yourself?

Answer 5

Ok. The actual question gives f(x), but it asks for f\[f ^{-1}(3)\] and \[f(f ^{-1}(2))\]. No I didn't come up with it myself. It was in my book for the "before calculus" section.

Answer 6

So far I got \[x=y(y^{4}+y^{2}+1)\]
and I don't know where to go from there.

Answer 7

solve \(x^5+x^3+x = 3\) and you'll get the inverse \(f^{−1}(3)\)

Answer 8

actually you don't need to do any work here
just notice that \(f\) eats \(f^{-1}\)

Answer 9

\[\require{cancel}\large{f(f^{-1}(3))\\~\\ \cancel{f}(\cancel{f^{-1}}(3)) \\~\\~\\3}\]

Answer 10

the inverse function "undoes" whatever the actual function does

Answer 11

I can see how that would apply to the second question. The answer would come out to two. But for the first question where it only ask for the inverse, should I just graph it and see what it comes out to?

Answer 12

Ahh no, just use irishboy's hint

Answer 13

ok thank you.

Answer 14

solve \(x^5+x^3+x = 3\) and you'll get the inverse \(f^{−1}(3)\)

is it hard to guess the \(x\) value that satisfies the above equation ?

Answer 15

I see it now. wow. Thanks again.

Answer 16

np