Question

Tried this one a couple times, I'll submit the answers I have, but my homework says I'm not getting ALL of them right
Let f(x) = x+1 and g(x) = 1/{x+1}. Then

(f of f) (x) = x^2+3+1

(f of g) (x) = x/(x^2+1)

(g of f) (x) = 1/(x^3+x+1)

(g of g) (x) = 1/(x^3+x^2)+1

Answer 1

Start with the first one, f of f.
There is no square in function f. How do you get an x^2 in the answer?

Answer 2

I did x(x)+1, which got me x^2+1 for the first f. Am I doing that wrong?

Answer 3

Start with f(x) = x+1

Answer 4

everywhere you see an x, replace it with f(x)

f(x) = x+1

f(x) = (x)+1

f( f(x) ) = ( f(x) )+1

then on the right side, replace f(x) with x+1, since f(x) = x+1

f( f(x) ) = ( f(x) )+1

f( f(x) ) = ( x+1 )+1

f( f(x) ) = x+1 +1

f( f(x) ) = x+2


So (f o f)(x) = x+2

Answer 5

So you don't multiply them together, you just replace the x with the x?

Answer 6

you replace x with f(x)

Answer 7

let's use f(x) and g(x)

Answer 8

(f o g) (x) is really f( g(x) )

Answer 9

to calculate f( g(x) ), we start with f(x)