Question

can some one show me how to do this the radical throws me off.
f(x) = sqrt(x-5), g(x) = sqrt(x+4)
find (g o f)(x) and give the domain

Answer 1

g is now a function of f(x), this means that you replace the x in g(x) by f(x)

so it looks like this
\[\sqrt{5(f(x))}\]

Answer 2

you know that f(x) = x^2 - 1, so you can substitute that in for f(x)

\[\sqrt{5(x^2 - 1)}\]

Answer 3

and the domain is all values of x that don't result in the number under the radical being negative

Answer 4

ok i had everything but the parentheses

Answer 5

yea just remember that x is replaced by EVERYTHING in f(x)

Answer 6

what do you do if you have 2 radicals?

Answer 7

that goes in too

and then use the rules of exponents to sort it out:

\[\sqrt{\sqrt{x}} = (x ^{1/2})^{1/2} = x ^{1/4}\]

Answer 8

\[=\sqrt[4]{x}\]

Answer 9

so if f(x)=sqrt{x-5) and g(x)= sqrt(x+4) then f of g would equal the sqrt of the sqrt(x+4)-5?

Answer 10

I think you got it, the way you wrote it can be interpreted in different ways
if you meant

\[\sqrt{\sqrt{x+4}-5}\]

Answer 11

then you got it

Answer 12

yea i meant that lol

Answer 13

yay good job :)

Answer 14

would the answer be the 4th root of x-1?