Hello sir

I need a full explanation of this sum

find domain and range of f(x)=|2x-3|-3

Asked by seeni2005 | 12th Oct, 2020, 08:50: PM

Expert Answer:

Given: f(x) = |2x - 3| - 3
f(x) is defined for all values of x
So, the domain of x is R
Now comma space straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 2 straight x minus 3 minus 3 comma space space space space space space 2 straight x minus 3 greater or equal than 0 end cell row cell negative left parenthesis 2 straight x minus 3 right parenthesis minus 3 comma space 2 straight x minus 3 less than 0 end cell end table close
When space 2 straight x minus 3 greater or equal than 0 space rightwards double arrow straight f left parenthesis straight x right parenthesis equals 2 straight x minus 3 minus 3 equals 2 straight x minus 6
As space 2 straight x minus 3 greater or equal than 0 space rightwards double arrow space 2 straight x minus 6 greater or equal than negative 3 space rightwards double arrow space straight f left parenthesis straight x right parenthesis greater or equal than negative 3
When space 2 straight x minus 3 less than 0 space rightwards double arrow straight f left parenthesis straight x right parenthesis equals negative left parenthesis 2 straight x minus 3 right parenthesis minus 3 equals negative 2 straight x plus 3 minus 3 equals negative 2 straight x
As space 2 straight x minus 3 less than 0 space rightwards double arrow space minus 2 straight x greater than negative 3 space rightwards double arrow straight f left parenthesis straight x right parenthesis greater than negative 3
Combining space the space two space we space get space space straight f left parenthesis straight x right parenthesis greater or equal than negative 3
Hence comma space the space range space of space straight f left parenthesis straight x right parenthesis space is space left square bracket negative 3 comma space infinity right parenthesis

Answered by Renu Varma | 13th Oct, 2020, 10:37: AM