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wolverine [178]
3 years ago
9

WILL GIVE BRAINLIEST!!!

Mathematics
2 answers:
frosja888 [35]3 years ago
5 0

Answer:

The answer below is actually correct.

Slav-nsk [51]3 years ago
4 0

\text{Consider the function}\\
\\
f(x)=6x^3-3\\
\\
\text{let }y=f(x), \text{ so we have}\\
\\
y=6x^3-3\\
\\
\text{now in order to find the inverse of the function, first we interchange x and y}\\
\text{so we get}\\
\\
x=6y^3-3

\text{now we will solve for y again and that will give the required inverse function.}\\
\text{so first we add 3 both sides to get}\\
\\
x+3=6y^3\\
\\
\text{now divide both sides by 6 to get}\\
\\
\frac{x+3}{6}=y^3\\
\\
\text{now take cube root both sides to get}\\
\\
\sqrt[3]{\frac{x+3}{6}}=\sqrt[3]{y^3}

\Rightarrow \sqrt[3]{\frac{x+3}{6}}=y\\
\\
\Rightarrow y=\sqrt[3]{\frac{x+3}{6}}\\
\\
\text{hence the inverse of the function is: }\\
\\
f^{-1}(x)=\sqrt[3]{\frac{x+3}{6}}

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