Some sums

1) Function is not invertible so the inverse cannot be found..

2) The remainder when the polynomial x+x³+x⁹+x²⁷+x⁸¹+x²⁴³ is divided by x² -1

x+x³+x⁹+x²⁷+x⁸¹+x²⁴³ =g(x)(x²-1) + ax+b

Now x=1,

6=a+b

x=-1

-6=-a+b

so a=6 and b=0

Hence the remainder will be 6x

3) If | x | + x + y =10
x + | y | - y =12

find x + y

Here we look at 4 different quadrants...

in the first quadrant, |x|=x and |y|=y
so in the 1st quadrant.. 2x+y=10
x=12
so x+y=-2

Now can you try the other 3 quadrants?