The value of N is a distance of two units from -1 on a number line which numbers could be the value of N

The absolute value of a number n is denoted by |n|.

It is defined as the distance between 0 (zero) and n (the number) on the number line.

Importantly, the absolute value of any nonzero number is always positive.

For example, |1.5| = 1.5 and |−1.5| = 1.5.

Both 1.5 and −1.5 have the same absolute value of 1.5, because 1.5 is 1.5 units from 0 (to the right) on the number line and −1.5 is 1.5 units from 0 (to the left).

Thus, |−n| = |n| for any nonzero number n, and |0| = 0

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!