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ElenaW [278]
3 years ago
15

Plz help me i need it

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
8 0

Answer:   \bold{d)\quad f^{-1}(x)=\dfrac{e^x}{5}}

<u>Step-by-step explanation:</u>

To find the inverse, swap the x's and y's and solve for y. <em>Note: f(x) is y</em>

<em>y = ln(5x)\\\\\text{Swap the x's and y's:}\\x=ln(5y)\\\\\text{Apply e to both sides:}\\e^x=e^{ln(5y)}\\\\e^{ln}\ \text{cancels out:}\\e^x=5y\\\\\text{Divide both sides by 5:}\\\dfrac{e^x}{5}=y\\\\\large \boxed{f^{-1}(x)=\dfrac{e^x}{5}}</em>

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