The function f(x)=x-2m+2. The value of x is greater than 0. The graph of the function does not intersect the x axis if for no value of x is the value of f(x) equal to 0.
`x - 2m + 2 != 0`
`x != 2m - 2`
Now as x > 0 , 2m - 2 > 0
or 2m > 2
m > 1
For values of m greater than 1, the graph of f(x)=x-2m+2, x>0 does not intersect the x axis.
If the graph of the function (which is a line) does not intercept the x axis, that means that the equation of the line has no real solutions.
In other words, there are no such values for x to cancel the equation of the line.
When the graph is intercepting x axis, then y = 0.
Let f(x) = y.
Since the graph is not intercepting x axis, then y > 0 =>
x-2m+2 > 0
We'll isolate x to the left side:
x > 2m - 2
Since x > 0 => 2m - 2 > 0
We'll divide by 2:
m - 1 > 0
m > 1
The interval of possible values for m, for the graph of f(x) not to intercept x axis, is: (1 , +infinite).