SOLUTION: Suppose f(x) = x^2+1 and g(x)=1-x. Then (fog)(-2) = ? Is it alright to ask for a solution for this, please? I have another item in my assignment similar to this that I want to b

Algebra ->  Functions -> SOLUTION: Suppose f(x) = x^2+1 and g(x)=1-x. Then (fog)(-2) = ? Is it alright to ask for a solution for this, please? I have another item in my assignment similar to this that I want to b      Log On


   

Question 1094526: Suppose f(x) = x^2+1 and g(x)=1-x. Then (fog)(-2) = ?
Is it alright to ask for a solution for this, please? I have another item in my assignment similar to this that I want to be able to solve myself. Thank you!
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are two ways to do it.

Solution 1 

First calculate g(-2) by substituting x= -2 into the formula g(x) = 1-x.  You will get

g(-2) = 1 - (-2) = 1 + 2 = 3.


Next calculate f(3) by substituting x= 3 into the formula f(x) = x^2 + 1.  You will get

f(3) = 3^2 + 1 = 9 + 1 = 10.


Thus (fog)(-2) = 10.

Solution 2 

(fog)(x) = f(g(x)) = f(1-x) = (1-x)^2 + 1   <<<---=== it is the general formula for f(g(x))


Now substitute x= -2 and calculate.


You will get the same answer 10.