Question

*****WHY U NO HELP ME??!!

Answer 1

\[f(x)= \frac{ 1 }{ x^4 -1}\] and \[g(x) = \sqrt[6]{x}\]

Answer 2

\[f(g(x)) = \frac{ 1 }{ (\sqrt[6]{x})^4 }-1\]

Answer 3

The radical and exponent part is confusing, how will I go about that?

Answer 4

@ganeshie8

Answer 5

you should convert radical to an exponent form

Answer 6

\[\huge\rm \sqrt[n]{x^m}=x^\frac{ m }{ n }\]index become the denomiantor of the fraction

Answer 7

denominator *

Answer 8

\(\color{blue}{\text{Originally Posted by}}\) @Fanduekisses
\[f(g(x)) = \frac{ 1 }{ (\sqrt[6]{x})^4 }-1\]
\(\color{blue}{\text{End of Quote}}\)
btw, -1 should be in the denominator

Answer 9

\[\huge\rm \frac{ 1 }{(\color{ReD}{ \sqrt[6]{x}} )^4} =\frac{ 1 }{ (\color{Red}{x^{??}})^4 }\]

Answer 10

\[\frac{ 1 }{ (x ^{1/6} )^4}\]

Answer 11

yes right now you can multiply 1/6 by 4
exponent rule \[\huge\rm (a^m)^x = a^{m \times x}\]

Answer 12

\[\frac{ 1 }{ x ^{2/3} }\]

Answer 13

don't forget the negative one

Answer 14

ok so the domain will be \[x \ge0 \] and

Answer 15

Wait how do I solve for x? \[x ^{2/3}= 1\]

Answer 16

The denominator part, to find the domain, what x cannot equal.

Answer 17

ugh sorry my laptop is acting up,slow net connection
alright so whats the question ? find domain ?

Answer 18

yes of the composition f(g(x))

Answer 19

you can take cube both sides to get rid of the fraction

Answer 20

like we rewrite x^2/3 into radical form \[\huge\rm \sqrt[3]{x^2}=1\] to cancel out cube root we should take cube sides
just like we take square root to cancel out square

Answer 21

wait be right back

Answer 22

btw, you can apply difference of squres....

Answer 23

\(\frac{ 1 }{ (\sqrt[6]{x})^4 }-1=\frac{1}{x^{2/3}}-1=x^{-2/3}-1=0\)
It doesn't change the answer in this case. lol

Answer 24

So th\[x \neq1 ?\]e domain of f(g(x)) is \[x \ge0\] and

Answer 25

Sorry for the late reply, I had an urgency.

Answer 26

how many solutions would you get when u take square root of something ?
and it's okay :=)

Answer 27

+- 1 hehe

Answer 28

:D got it now hehe thanks so much!

Answer 29

So the domain is x cannot equal +-1 and x has to be greater than or equal to 0 ?

Answer 30

to write in interval u can draw a number line