Exam doubt

let f(x) = 3x+5 and g(x) = 7x+3

fog(x) = 3(7x+3)+5

and gof(x) = 7(3x+5)+3

I hope you understood the logic

Originally posted by : Roshan Thomas
	let f(x) = 3x+5 and g(x) = 7x+3 fog(x) = 3(7x+3)+5 and gof(x) = 7(3x+5)+3 I hope you understood the logic

correctly explained....

to elaborate

while calculating fog(x) - substitute x with value of g(x)

and similarly for gof(x)- substitute x with f(x)

what is domain of the function.?

Taking my initial example

f(x) = 3x+5

here domain of the function is the values that x can take (it depends on the situation actually, you can define it to be real numbers, integers, fractions, complex number etc...)

and the solution that you get for the domain of x is called the Range/Image

For example 

f(x) = 1/x

when domain is Real numbers then solution is not defined for x=0, so the domain should be R-[0] , i.e all real numbers excluding 0, to get a valid solution

Again

f(x) = sqr rt of x

here if the domain is real numbers then the range will be real numbers, the function is not defined for x<0, because the domain excludes complex numbers

Range is the result of solving the function. 

Depending on the range the domain should exclude numbers for which range is not defined

what is reflexive,symmetric, transitive,equivalence function??