Hello sir,

Please explain this sum,

Find the domain of the functions

i) f(x) = 1/√(x^2 -5x + 6) 

ii) f(x) = x^2+2x+1/x^2-8x+12

Asked by seeni2005 | 21st Sep, 2020, 03:04: PM

Expert Answer:

To find the domain of the function f(x) = 1/sqrt{x2-5x+6}
The space function space straight f space is space defined space only space when space the space denominator space not equal to 0 space and space square root of straight x squared minus 5 straight x plus 6 end root space is space defined
Therefore comma space straight f left parenthesis straight x right parenthesis space is space defined space when space straight x squared minus 5 straight x plus 6 greater than 0
straight x squared minus 3 straight x minus 2 straight x plus 6 greater than 0
straight x left parenthesis straight x minus 3 right parenthesis minus 2 left parenthesis straight x minus 3 right parenthesis greater than 0
left parenthesis straight x minus 3 right parenthesis left parenthesis straight x minus 2 right parenthesis greater than 0
rightwards double arrow straight x minus 3 greater than 0 space and space straight x minus 2 greater than 0 space space OR thin space space straight x minus 3 less than 0 space and space straight x minus 2 less than 0
rightwards double arrow straight x greater than 3 space and space straight x greater than 2 space OR space space straight x less than 3 space and space straight x less than 2
rightwards double arrow straight x greater than 3 space space OR space space straight x less than 2
rightwards double arrow straight x element of open parentheses 3 comma space infinity close parentheses thin space thin space OR thin space thin space straight x element of open parentheses negative infinity comma space 2 close parentheses
rightwards double arrow thin space straight x element of open parentheses negative infinity comma space 2 close parentheses union open parentheses 3 comma space infinity close parentheses

Answered by Renu Varma | 22nd Sep, 2020, 12:27: PM