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alexdok [17]
2 years ago
9

F(x) = 5/(7x-8) What is the inverse of this function?

Mathematics
2 answers:
oee [108]2 years ago
3 0
f(x)=\dfrac{5}{7x-8}\\\\y=\dfrac{5}{7x-8}\iff\dfrac{1}{y}=\dfrac{7x-8}{5}\ \ \ |multiply\ both\ sides\ by\ 5\\\\\dfrac{5}{y}=7x-8\ \ \ |add\ 8\ to\ both\ sides\\\\7x=\dfrac{5}{y}+8\\\\7x=\dfrac{5}{y}+\dfrac{8y}{y}\\\\7x=\dfrac{5+8y}{y}\ \ \ \ |divide\ both\ sides\ by\ 7\\\\x=\dfrac{5+8y}{7y}\\\\Answer:\boxed{f^{-1}(x)=\dfrac{5+8x}{7x}\ other\ form\ f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}
zzz [600]2 years ago
3 0
f(x)=\dfrac{5}{7x-8}\\
y=\dfrac{5}{7x-8}\\
7x-8=\dfrac{5}{y}\\
7x=\dfrac{5}{y}+8\\
x=\dfrac{5}{7y}+\dfrac{8}{7}\\
\boxed{f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}

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Step-by-step explanation:

                     ~ Distribute:

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                        ~ Flip the equation:

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                          ~ Use transposition method:

                     (take -3 / 2 to the other side)

                       1 / 2 x = -11 - (-3 / 2)

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Hope this helped

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