For any function f(x), the inverse function f-1(x)is defined. If f(x)=3e-x
, then f-1(x)=?
a)ln(3/x) b) ln(x/3)
c) ln(x).5 d) (1/3)ln(x)
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Answer / Abdhesh Kumar
To find the inverse function (f^-1(x)), we can use the method of solving for x in terms of f(x). In this case, we have f(x) = 3e^(-x), so we want to solve for x in terms of f(x):
ln(f(x)) = ln(3e^-x)
ln(f(x)) = ln(3) - x
Now we can use the inverse function property:
f^-1(x) = e^(ln(x + constant))
In this case, the constant is -ln(3), so we have:
f^-1(x) = e^(ln(x) - ln(3))
f^-1(x) = (e^ln(x)) / (e^ln(3))
f^-1(x) = x * (1/3)
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