How do I do these kinds of problems? given the following functions find f(g(9))
f(x)=1/x-10 and g(x)=1/x

Question

How do I do these kinds of problems? given the following functions find f(g(9))
f(x)=1/x-10 and g(x)=1/x

ranga · Answer

Find g(9) first.  Then put that as x in f(x)=1/x-10 and evaluate f(x).

ranga · Answer

g(x) = 1 / x
g(9) = ?

anonymous · Answer

g(9)=9

anonymous · Answer

=1/9

ranga · Answer

Yes. g(9) = 1/9
f(g(9)) = f(1/9)
If f(x) = 1/x-10
f(1/9) = ?

anonymous · Answer

my answer is -89/9

ranga · Answer

no. x should be replaced by 1/9 not 9.

ranga · Answer

If a is divide by a fraction b/c it is the same as flipping the fraction and multiplying.
a divided by b/c = a * c / b = ac/b

anonymous · Answer

-9/89:?

ranga · Answer

f(x) = 1/x-10
Put x = 1/9 in 1/x-10
= 1 / (1/9) - 10
= 1 * 9/1  -  10
= 9 - 10
= -1

 f(g(9)) = -1

anonymous · Answer

that's not one of my answers . Do I have to do anything next?

ranga · Answer

you probably forgot to put parenthesis in your problem.  
Did f(x) look likes this:$$f(x) = \frac{ 1 }{ x - 10 }$$or like this:$$f(x) = \frac{ 1 }{ x } - 10$$.When writing if you don't use a parenthesis it will be taken as the latter which is what I did.

anonymous · Answer

the first one

ranga · Answer

yeah.  Then you should write it like this: f(x) = 1/(x-10) 
The parenthesis tell us that the whole thing is in the denominator.

Anyway, from the start the problem looks like this:
g(x)=1/x
g(9) = 1/9 
f(g(9)) = f(1/9)

f(x) = 1/(x-10)
f(1/9) = 1 / (1/9 - 10)
To get rid of the 9 as a fraction, multiply top and bottom by 9
= 9 * 1 / (9 * 1/9  -  9 * 10)   = 9 / (1 - 90) = 9/(-89) = - 9/89

anonymous · Answer

ty! very much!