Question

Find f∘g and g∘f,
and the domain of f∘g.
where
f(x)=√(x+4) , g(x)=x^2

Answer 1

I got f o g as \[\sqrt{x ^{2}+4}\]

Answer 2

and g o f as x+4

but am confused about the domain of f o g.....

according to me it should be \[x \ge -4\]
but the book says it should be "all real numbers"

if the book's answer is correct then why is it correct??

Answer 3

Fog(x)=\[\sqrt{x^{2}+4}\]
Gof(x)=x+4
now,.,.. as far as the domain of F0g(x) is concerned,, then U should know what is domain.... Set of all the possible values that an in dependent variable may take... Or the set of all the values for which the function is defined..
Right..... NOw U can see... If u put -99... U will get answer... if u put -1 u will get the answer... If u put any positive integer U will get the answer... So domain will be all real numbers....... :)

Answer 4

but in composite functions we have to consider the domains of original functions as well...

Answer 5

brother any number squared gives a positive number. as such any number (real) added to the integer in fog gives a real positive number.

Answer 6

and for original f(x), we cannot have x less than -4 otherwise we wil get a negative underroot...

Answer 7

U have asked about the domain of the Fog(x)... not of f(x)....... I don't think so,, If u have to find the domain of fog(x), then U have to consider the actual functions.

Answer 8

My book "Precalculus With Limits" says

"The domain of fog is the set of all x in the domain of g such that g(x) is in the domain of f."
and as I pointed out earlier, the domain of f cannot be numbers less than -4.

Answer 9

OK OK i got it

Answer 10

no it does not need...fog is an entirely different nd indpendent function

Answer 11

So, where's the problem.... Ur book says.... The domain of fog(x) is the set of all x in the domain of g(x)... So also g(x) has domain all real numbers... and so for f(x) x greter and equal to -4 ....

Answer 12

waleed is that nessacary? have u heard....i dnt kno of such condition

Answer 13

@waleed_imtiaz

As I said above, while writing down the definition I realised my mistake. It is all values of g... and for g all values of x are valid and so in turn all values valid for fog........Thanks for helping out.....

Answer 14

yes.... Now u are rite..... ANd @amriju the new function is totally independent i think so.... willn't depend on the actual funtions

Answer 15

yeah...evn i think so...thanks bro

Answer 16

my pleasure...... :D

Answer 17

I suggest you should visit this site which tells about domains of composite functions..
http://www.sinclair.edu/centers/mathlab/pub/findyourcourse/worksheets/116,117/CompositeFunctionsAndTheirDomains.pdf