Question

f(x)= sqrt(4-x) and h(x)=x^2
Find the simplified formula for this combination function and domain: (foh)(x) and (fof)(x)

Answer 1

\[f(x)=\sqrt {4-x} \]

Answer 2

I thought it was \[\sqrt{4-x^2}\]

Answer 3

Well Doesnt Look Like That :)

Answer 4

Oh okay, lol I don't get why the answer is just something thats already given lol, explainnn please? Like your steps

Answer 5

\[(foh)(x)=\sqrt{4-(x)^2}\]

Answer 6

\[(fof)x=\sqrt{4-(4-x)}\]

Answer 7

Got It @jessicardoza93

Answer 8

(hof)(x)?

Answer 9

@hba Thanks :)

Answer 10

\[(hof)x=(\sqrt{4-x})^2\]

Answer 11

Grazie :)

Answer 12

what about the domains?

Answer 13

What Do You Mean ?

Answer 14

Hey I was right on the (foh) :P hah, uhm im not sure it says "In each case say what the domain is "

Answer 15

Please Dont Confuse Me LoL And Be Clear ;)

Answer 16

notice that h(f(x)) simplifies to 4-x
however, in the original with the square root, you must exclude x values that give you a negative number inside the root sign.

Answer 17

Given: f(x)= sqrt(4-x) and h(x)=x^2
Problem: Find the simplified formula for this combination function and for each case state what the domain is
a)(foh)(x)
b)(fof)(x)

@hba thats as clear as I can be :)

Answer 18

@phi what does that mean then... ?

Answer 19

\[(fof)x=\sqrt{4-(4-x)},(fof)x=\sqrt{-x}\]

Answer 20

f(f(x)) is
\[ \sqrt{4-\sqrt{4-x}} \]
first 4-x must be ≥0 or the inside square root will be the root of a neg number
4-x≥0 4≥x
now the outer root you need 4- sqrt(4-x) ≥0
4≥ sqrt(4-x)
16≥ 4-x
12≥ -x
multiply by -1 and flip the ≥
-12 ≤ x
so
-12≤ x ≤4

Answer 21

for (a) f(h(x))
\[\sqrt{4-x^2} \]
you need to find the values of x that keep 4-x^2 ≥0

Answer 22

@phi so -12≤ x ≤4 is the answer for (fof)(x)?

Answer 23

that is the domain for (f o f) (x)

Answer 24

thank you !!!