Problem solving

[ccraftal@yahoo.com]

f(x)=x2+2x-1, g(x)=x2-2x-1 (fog)(-2)

 

[Brainwave]

solution

F(x)= x^2 + 2x - 1, g(x)= x^2 - 2x - 1

Fog is by puting the value of g(x) in x-variable of f(x)

So, fog = (x^2 - 2x - 1)^2 + 2(x^2 - 2x - 1) - 1

When you simplify you have

fog= x^4 - 4x^3 + 4x^2 - 2

fog(-2) = (-2)^4 - 4(-2)^3 + 4(-2)^2 - 2 = 16 + 32 + 16 - 2 = 62

 

[stapel]

F(x)= ....

There is no "F(x)". Let's please not encourage incorrect (and confusing!) notation.

Fog is by puting the value of g(x) in x-variable of f(x)

No: "(f o g)(x)" is inserting the formula for g(x) in for the x-variable in the formula for f(x). It's called "function composition". Part of helping students is using standard notation; it not only encourages proper lingo, but also avoids confusion, especially for beginners.

It should be noted, by the way, that the student asked about (f o g)(-2), so it might be helpful to mention that in your response, too. Thank you!

 

[lookagain]

f(x)=x2+2x-1, g(x)=x2-2x-1 (fog)(-2)

\(\displaystyle f(x) = x^2 + 2x - 1, \ \ \ g(x) = x^2 - 2x - 1\)

Find (f o g)(-2).


You don't have to find the explicit composite function at all. You can bypass that.

(f o g)(-2) =

f(g(-2))

First work out g(-2):

g(-2) =

\(\displaystyle (-2)^2 - 2(-2) - 1 = \)

4 + 4 - 1 =

7


So f(g(-2)) = f(7)


Then the answer to the original question is


\(\displaystyle (7)^2 + 2(7) - 1 \)=

49 + 14 - 1 =


\(\displaystyle \boxed{ \ 62\ }\)