interpolation to abscissa

It's fairly clear from the documentation that approxfun() will not
extrapolate.

help.search("extrapolate")
library(Hmisc)
?approxExtrap

Some sort of minimization approach:

 > approxExtrap(x=c(0,5,10,15,20), y=c(16,45,77,101,125),xout=c(-4,0,4))

$x
[1] -4  0  4

$y
[1] -7.2 16.0 39.2

 > approxExtrap(x=c(0,5,10,15,20),

y=c(16,45,77,101,125),xout=seq(-2.8,-2.6, by=0.01))
$x
  [1] -2.80 -2.79 -2.78 -2.77 -2.76 -2.75 -2.74 -2.73 -2.72 -2.71
-2.70 -2.69 -2.68
[14] -2.67 -2.66 -2.65 -2.64 -2.63 -2.62 -2.61 -2.60

$y
  [1] -0.240 -0.182 -0.124 -0.066 -0.008  0.050  0.108  0.166  0.224
0.282  0.340
[12]  0.398  0.456  0.514  0.572  0.630  0.688  0.746  0.804  0.862
0.920

How accurate do you need the answer?

I tried Hmisc's inverseFunction(), but it returned 0 for an argument
of zero:

 > invF <- inverseFunction(x=c(0,5,10,15,20), y=c(16,45,77,101,125))
 > invF(0)

So I then hacked Harrell's inverseFunction by substituting
approxExtrap in every in instance
where approx appeared, creating invFunc2:

then

 > invF <- invFunc2(x=c(0,5,10,15,20), y=c(16,45,77,101,125))
 >
 > invF(0)

[1] -2.758621