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Which function is the inverse of f(x)=50,000(0.8)^x?
a. f^-1(x)=log0.8(x/20,000)
b. f^-1(x)=log50,000(x/0.8)
c. f^-1(x)=log0.8(50,000/x)
d. f^-1(x)=log0.8(x/50,000)

Respuesta :

hello7people
I think that it is B because I'm pretty sure it has to be log of 50,000. But I forgot how to get the rest of it but B is the only one with log of 50k.
f(x) = 50,000 (0.8)^x

⇒ y = 50,000 (0.8)^x
⇒ log y = log 50,000 + x log 0.8
⇒ x log 0.8 = log y - log 50,000 = log (y/50,000)
⇒ x = log(y/50,000) / log 0.8
⇒ x = log0.8(y/50,000)

 ⇒ f^-1(x)=log0.8(x/50,000)

Answer is D

Hope it helps!

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