Does this make the function Transcendental?

[sponsoredwalk]

Hi I'm reading Euler's Introduction to Analysis of the Infinite & he's distinguishing between algebraic & transcendental functions and I wonder is the fact that the following function cannot be written explicitly a cause of "transcendentality".

Z^5 = az^2Z^3 - bz^4Z^2 + cz^3Z - 1

where Z is a function of z.

Maybe I've read it wrong or asked the question too soon but does being unable to write a function explicitly automatically make the answer transcendental?

 

[HallsofIvy]

I have moved this thread to "Calculus and Analysis" because it is question, not "learning materials".

 

[IttyBittyBit]

Why don't you read it more carefully this time? He clearly states what makes a function transcendental or no.

http://en.wikipedia.org/wiki/Transcendental_function