1. combining functions part 2

If:
f (x) = 3(x+1)^2 (the last 2 means square)
h(x) = 2/3 Ö(1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

what is (h o f)(x)??

Thank you very much .

2. Originally Posted by zdenka
If:
f (x) = 3(x+1)^2 (the last 2 means square)
h(x) = 2/3 Ö(1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

what is (h o f)(x)??

Thank you very much .
$(hof)(x)=h(f(x))$

$f(x)=3(x+1)^2=3x^2+6x+3=t$

$\implies (hof)(x)=h(f(x))=h(t)=\frac 23 \sqrt{1-t} +3$

$=\frac 23 \sqrt{1-(3x^2+6x+3)}+3=\frac 23 \sqrt{-3x^2-6x-2}+3=\dots$

3. Originally Posted by zdenka
If:
f (x) = 3(x+1)^2 (the last 2 means square)
h(x) = 2/3 Ö(1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

what is (h o f)(x)??

Thank you very much .
$f(x)=(3x+1)^2$

$g(x)=(1-x)^{\frac{2}{3}}+3$

Are these the equations you meant to type?

If so, plug f(x) in for x in the g(x) equation like so:

$g(x)=(1-f(x))^{\frac{2}{3}}+3$

$g(x)=(1-(3x+1)^2)^{\frac{2}{3}}+3$

4. Originally Posted by zdenka
If:
f (x) = 3(x+1)^2 (the last 2 means square)
h(x) = 2/3 Ö(1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

what is (h o f)(x)??

Thank you very much .
$f(x)=3(x+1)^2$

$h(x)=\frac23 \cdot \sqrt{1-x} + 3$

$(h\circ f)(x)=h(f(x))$

That means replace the x in h by the term of f:

$h(f(x))= \frac23 \cdot \sqrt{1-3(x+1)^2} + 3$

Try to simplify the last term - but it isn't necessary according to the wording of your question.

5. Sorry about the wording.... I need to simplify it too....