inline definition causes unresolved symbols in program

Question

So I have the following code:

#include <stdio.h>

#define MAX(a,b) (a) > (b) ? a : b

int abs(int a)
{
    if (a > 0)
        return a;
    else
        return a*-1;
}

inline int avg(int a, int b)
{
    return (a+b)/2;
}

int math_max(int a, int b)
{
    return (avg(a,b)+abs(avg(a,b)-b));
}

int main(int argc, char** argv)
{
    return 0;
}

When I compile it: gcc -g test.c -o test I get:

/tmp/ccZbHEju.o: In function `math_max':
test.c:(.text+0x33): undefined reference to `avg'
test.c:(.text+0x44): undefined reference to `avg'
collect2: error: ld returned 1 exit status

I can fix this by removing the inline notation from avg, but I don't know why I'm getting undefined references if its inline - I thought the compiler was supposed to take care of that

Anyone care to explain?

** Adding more information **
For those who can't reproduce, I'm using:
gcc --version gcc (GCC) 5.3.0 Copyright (C) 2015 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Compiling this code with without linking generates the following:

[ishaypeled@arania test]$ gcc -c test.c -o ./test.o
[ishaypeled@arania test]$ readelf -s ./test.o

Symbol table '.symtab' contains 13 entries:
   Num:    Value          Size Type    Bind   Vis      Ndx Name  
     0: 0000000000000000     0 NOTYPE  LOCAL  DEFAULT  UND   
     1: 0000000000000000     0 FILE    LOCAL  DEFAULT  ABS test.c  
     2: 0000000000000000     0 SECTION LOCAL  DEFAULT    1   
     3: 0000000000000000     0 SECTION LOCAL  DEFAULT    3   
     4: 0000000000000000     0 SECTION LOCAL  DEFAULT    4  
     5: 0000000000000000     0 SECTION LOCAL  DEFAULT    6  
     6: 0000000000000000     0 SECTION LOCAL  DEFAULT    7  
     7: 0000000000000000     0 SECTION LOCAL  DEFAULT    5  
     8: 0000000000000000    25 FUNC    GLOBAL DEFAULT    1 abs  
     9: 0000000000000019    43 FUNC    GLOBAL DEFAULT    1 max  
    10: 0000000000000044    69 FUNC    GLOBAL DEFAULT    1 math_max  
    11: 0000000000000000     0 NOTYPE  GLOBAL DEFAULT  UND avg  
    12: 0000000000000089    18 FUNC    GLOBAL DEFAULT    1 main 

Which clearly shows avg as NOTYPE and UND - this is why the linker failed... I have no idea why that happens. I also examined the preprocessor output from gcc:

[ishaypeled@arania test]$ gcc test.c -E

# 5 "test.c"
int abs(int a)
{
    if (a > 0)
        return a;
    else
        return a*-1;
}

int max(int a, int b)
{
    return ((a+b)+abs(a-b))/2;
}

inline int avg(int a, int b)
{
    return (a+b)/2;
}

int math_max(int a, int b)
{
    int avg_calc = avg(a,b);
    int distance_from_avg = abs(avg_calc-a);
    int res = avg_calc+distance_from_avg;
    return res;
}

int main(int argc, char** argv)
{
# 44 "test.c"
    return 0;
}

Looks perfectly fine, avg appears before the usage in math_max.

STDC version: 201112 __GNUC__ defined