Question

Use algebra to find the inverse of the given one-to-one function.
f(x) = (x5 + 3)3

Answer 1

the 3 outside the parenthesis is ^3

Answer 2

you have a function that, given any value for x, will give you what the value fo f(x) should be.
what they are asking you is to find the inverse. in other words, re-arrange the equation so that given the values of f(x), you can find what x is.

Answer 3

i had a similar prob on my hw... f(x)=-2x+7 and i got x-7/-2 which was correct

Answer 4

this ones different looking though

Answer 5

given this:\[f(x)=(x^{5}+3)^{3}\]re-arrange to get:\[x=...\]

Answer 6

I'll show you how to do this one which should help you understan (I hope)

Answer 7

ok

Answer 8

\[f(x)=(x^{5}+3)^{3}\]swap LHS and RHS:\[(x^{5}+3)^{3}=f(x)\]take cube root of both sides:\[x^{5}+3=\sqrt[3]{f(x)}\]take 3 away from both sides:\[x^{5}=\sqrt[3]{f(x)}-3\]take the fifth root of both sides:\[x=\sqrt[5]{\sqrt[3]{f(x)}-3}\]now re-write in standard form so that it looks like a standard function. you do this by replacing f(x) with x and x with g(x) which is now your inverse function:\[g(x)=\sqrt[5]{\sqrt[3]{x}-3}\]

Answer 9

to check it, try some random value, say x=0
\[(0^{5}+3)^{3}=(3)^{3}=27\]
so g(27) should give us 0, lets check:
\[\sqrt[5]{\sqrt[3]{27}-3}=\sqrt[5]{3-3}=0\]

Answer 10

Thanks a lot. I really appreciate it!