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Find the inverse

find the inverse, f-1(x). For the equation f(x)=2e3x+1
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1 Answer

f(x) = 2e3x+1
y = 2e3x+1
To find the inverse function, f-1(x), swap the x's and y's and solve for y:
x = 2e3y+1
x-1 = 2e3y
(1/2)(x-1) = e3y
ln[(1/2)(x-1)] = 3y              [take the ln of both sides]
(1/3)(-ln(2)+ln(x-1)) = y      [ln(1/2) = ln(2-1) = -ln(2), ln(ab) = ln(a) + ln(b)]
y = f-1(x) = (1/3)ln(x-1) - (1/3)ln(2)