Name: Brandie

Who is asking: Teacher

Level: All

Question:

Could you please tell me what is the basic guideline for inverting a function

Example:

S(R)=2PiRal

V(R)=PiR(squared)bl

R(V)=?

help please I am stuck...
Thank you!

Hi Brandie,
For V(R) = Pi*R(squared), you proceed as follows:

- Suppose the function is written on the x-y axis, with x = R and
y = V(R):

y = Pi*x^{2}

- Solve for x (that is, isolate x):

y/Pi = x^{2}

- Now your x is R(V) and y is V:

That's it, you have inverted the function. It becomes easy
once you get the hang of it. Mathematicians think, in the
first case, of V(R) as being a function of the independent
variable R, and in the second case of R(V) as a function of the
independent variable V. The name given to a variable is not
important: You could as well write V(x) = Pi*x^{2}
or V(t) = Pi*t(squared) or so on, and it would mean the same
as V(R) = Pi*R^{2} (just like subroutines incomputer programs).
However it is very important to write V(x) rather than just V, to indicate
that it is a function in that variable.

Physicists have a different viewpoint. They would simply
write V = Pi*R^{2} and view it as a relation between
the quantities V and R. of course this relation is the
same as the one expressed by the equation R = square root of{V/Pi},
that is, they may not see the point of making such a big fuss
about "inverting functions". On the other hand they do not like
to change the name of their variables: t should always mean time,
T temperature, and so on.

Cheers,

Claude