Please explain why the range is x7 fx2x7 If I plug in for ex

Please explain why the range is x>7. f(x)=2x+7 If I plug in, for example 6, x = 19.

Solution

f(x)=2x+7
here domain is all real value of x because we can put x as anything we like and
Range here is also all real because when we put any random value of x we will get some random value of y and for x varying from -infinity to infinity our y will also vary from -infinity to infinity.

but if it is given that x>0 then our range will be y>7 because x>0 means you can take x as low as 0.00001 and then 2(0.00001)+7=7.00002 which is greater than 7
so our range will be y>7

also see the example you took x=6 in that case our y=19
because f(x)=2*6+7=12+7=19
which is f(x)=19 or y=19