SOLUTION: Let f(x)=x^2-1 and g(x)=1-2x Find the indicated values f(g(-1)) and g(f(-1) I have 4 of these types of questions on my homework and have no idea how to solve them. This is the fi

Algebra ->  Systems-of-equations -> SOLUTION: Let f(x)=x^2-1 and g(x)=1-2x Find the indicated values f(g(-1)) and g(f(-1) I have 4 of these types of questions on my homework and have no idea how to solve them. This is the fi      Log On


   

Question 647815: Let f(x)=x^2-1 and g(x)=1-2x Find the indicated values
f(g(-1)) and g(f(-1) I have 4 of these types of questions on my homework and have no idea how to solve them. This is the first one so there is other equation to help! Thanks!!
Answer by Algebraic(50) About Me  (Show Source):
You can put this solution on YOUR website!
You need to plug in the inner value first and then you can do it all together.
Original equations: f%28x%29=x%5E2-1 and g%28x%29=1-2x
Find f%28g%28-1%29%29 and g%28f%28-1%29%29
Step 1: We'll begin by doing this equation first: f%28g%28-1%29%29
You're going to want to solve g%28-1%29 first.
g%28-1%29=1-2%28-1%29
Step 2: Simplify
g%28-1%29=1%2B2
g%28-1%29=3
So, now we know that g%28-1%29=3, so let's replace '3' into the f%28x%29=x%5E2-1 equation.
Step 1: Replace '3' into the equation
f%283%29=3%5E2-1
Step 2: Simplify
f%283%29=9-1
f%283%29=8
The answer to f%28g%28-1%29%29 is 8.
Let's do the other equation now (g%28f%28-1%29%29)
You're going to want to solve f%28-1%29 first.
Step 1: Replace '-1' into the f(x) equation
f%28-1%29=%28-1%29%5E2-1
f%28-1%29=1-1
f%28-1%29=0
Now we know that f%28-1%29=0, so let's replace '0' into the g%28x%29=1-2x equation.
Step 1: Replace '0' into the equation
g%280%29=1-2%280%29
Step 2: Simplify
g%280%29=1-0
g%280%29=1%29
The answer to g%28f%28-1%29%29 is 1.