Question

Instructions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Consider the functions f(x)=x^2+9x and g(x)=1/x.
f(g(-1)) is
g(f(1/2)) is

Answer 1

`f(g(x))=1/x^2+9/x\Rightarrow f(g(-1))=-8`


`f(g(x))=1/(x^2+9x) \Rightarrow g(f(1/2))=4/19`

Answer 2

-8

2/19

Explanation:

We must substitute x=-1 into g(x) and then the answer of g(x) we must substiute as x into f(x). Similarly we must substitute x=1/2 into f(x) and the answer as x into g(x):

1. x=-1 into g(x)

`=1/-1=-1`

substitute x=-1 into f(x)

`=(-1)^2+9\cdot(-1)=-8`

2. x=1/2 into f(x)

`=(1/2)^2+9\cdot(1/2)=19/2`

substitute x=19/2 into g(x)

`=1/(11/2)=2/19`