Let G be a family of real functions f:**R**-->**R**.
In the paper we examine the following question:
for which families F of real functions does there exist
g:**R**-->**R**
such that f+g belongs to G for all f from F?
More precisely, we will study a cardinal
function add(G) defined as the smallest cardinality of a family
F of real functions for which there is no such g.
We prove that
$add(ext)=add(pr)=c+$
and $add(pc)=2c$,
where c denotes the cardinality of the continuum,
and ext, pr and pc stand for the classes of extendable functions,
functions with perfect road and peripherally continuous functions
from **R** into **R**, respectively.
In particular, equation
$add(ext)=c+$
implies immediately
that every real function is a sum of two extendable functions.
This solves a problem of Gibson.

We also study the multiplicative analogue mul(G) of the function add(F) and prove that mul(ext)=mul(pr)=2 and add(pc)=c.

**Requires rae.cls and
epic.sty files. **
Uses amstex.sty and amssymb.sty

**DVI
and Postscript files** are available at the
**Topology Atlas**
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