Inverse-Function Solver - HP 48gII Advanced User's Reference Manual

Inverse-Function Solver

This section describes the program ROOTR, which finds the value of x at which f(x) = y. You supply the
variable name for the program that calculates f(x), the value of y, and a guess for x (in case there are multiple
solutions).
'function name'
Techniques used in ROOTR
Programmatic use of root-finder. ROOTR executes ROOT to find the desired x-value.
!
Programs as arguments. Although programs are commonly named and then executed by calling their
!
names, programs can also be put on the stack and used as arguments to other programs.
ROOTR program listing
Program:
«
 fname yvalue xguess Creates local variables.
«
xguess 'XTEMP' STO
« XTEMP fname
yvalue - »
'XTEMP'
xguess
ROOT
»
Program:
'XTEMP' PURGE
»
`OROOTR K
Checksum: # 4708d
Bytes: 163
Example: Assume you often work with the expression
3 2
3.7x + 4.5x + 3.9x + 5 and have created the program X"FX to calculate the value:
«  x '3.7*x^3+4.5*x^2+3.9*x+5' »
You can use ROOTR to calculate the inverse function.
2-38 RPL Programming Examples
Level 3 Level 2
y
Level 1 "
"
x
guess
Comments:
Begins the defining procedure.
Creates variable XTEMP (to be solved for).
Enters program that evaluates f(x) - y.
Enters name of unknown variable.
Enters guess for XTEMP.
Solves program for XTEMP.
Ends the defining procedure.
Comments:
Purges the temporary variable.
Stores the program in ROOTR.
Level 1
x