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matrenka [14]
3 years ago
13

Find a formula for the inverse of the function. f(x) = e^6x − 9

Mathematics
1 answer:
STatiana [176]3 years ago
7 0

Answer:

f^{-1}(x)=\frac{1}{6}\ln(x+9)

Step-by-step explanation:

So we have the function:

f(x)=e^{6x}-9

To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:

x=e^{6f^{-1}(x)}-9

Add 9 to both sides:

x+9=e^{6f^{-1}(x)}

Take the natural log of both sides:

\ln(x+9)=\ln(e^{6f^{-1}(x)})

The right side cancels:

\ln(x+9)=6f^{-1}(x)

Divide both sides by 6:

f^{-1}(x)=\frac{1}{6}\ln(x+9)

And we're done!

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