Help finding the inverse...?

Question

Find a formula for the inverse of the function.

f(x) = e^x^9

Answer 1

y = e^( x^ ( 9 ) )

Replace x with y, then solve for y.

x = e^( y^ ( 9 ) )

Take the natural log of both sides.

ln (x) = ln e^( y^ ( 9 ) )

ln (x) = y^9

9√( ln (x) ) = y

y = 9√( ln (x) )

y equals the ninth root of the natural log of x.

You might have some trouble entering that in the calculator. In that case

y = [ ln (x) ]^(1/9)

Answer 2

if y=e^x^9 then to find the inverse switch x and y and solve for y.

x=e^y^9

ln x = y^9

y=(ln x ) ^1/9

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Answer 3

f(x)=e^x^9

Write: y=e^x^9

Solve for x

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