Find the inverse of the function. f(x) = cube root x/8 -4

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Find the inverse of the function. f(x) = cube root x/8 -4

Mathematics
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is that \(f(x)=(\sqrt[3]x/8) -4\) ?
\[f(x)=\sqrt[3]{\frac{ x }{ 8 }}-4\]
oh, ok to get the inverse let y= f(x) and interchange 'x' and 'y'

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just solve for x and at the end swap x and y.
\(y= \sqrt[3]{\dfrac{x}{8}}-4\\x= \sqrt[3]{\dfrac{y}{8}}-4\) solve for 'y' ! can you ?
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maybe start with cuping both sides?
ADD 4 and then cube both sides :)
same thing :P
\[x ^{3}=\frac{ y }{ 8 } -4\]
no, no.... we first would need to add 4 on both sides... first do that before cubing.
Oh...
BUt adding 4 first will be easier :P
\[x+4=\sqrt[3]{\frac{ x }{ 8}}\]
\[x+4^{3}=\frac{ x }{ 8 } ?\]
looks fishy.
when you cube , you cube entirely, so it'll be (x+4)^3 = y/8 right ?
yea
now what you can do to isolate 'y' ?
multiply by 8
correct! do that and tell me what u get ?
(x+40)^3=y?
no, sorry
\[f ^{-1}(x)=8(x+4)^{3}\]
correct! good :)
remember do entirely. WHen you + / * square or cupe you do it to whole side.
1 tip use parenthesis a+b=c+d if they tell you divide both sides by t a+b=c+d (a+b)/t=(c+d)/t use perenthesis cuzz that says do it to whole thing --- another tip If told to square both sides a+b=c+d (a+b)^2=(c+d)^2 but (a+b)^2=(c+d)^2 is not a^2+b^2=c^2+d^2 it is (a+b)*(a*b)=(c+d)*(c+d) Maybe you knew but lots of people assume or forget.

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