Question

f(x)=√(x+8) and g(x)=4x
a) domain of f(g(x))
b) domain of g(f(x))

Answer 1

all the real numbers

Answer 2

for both?

Answer 3

yess i believe so

Answer 4

let's see what @cwrw238 writes..she is more precised

Answer 5

could you show the working out?

Answer 6

ok

Answer 7

f(g(x)) = √(4x+8)
now a square root of a negative number is not real
so the domain is x >= -2 or [-2,+INF)

Answer 8

is it -2 because -2 is the smallest negative number?

Answer 9

\[f(g(x))= \sqrt{4x+8}=2\sqrt{x+2}\] and \[g(f(x))= 4\sqrt{x+8}\] so these are not defined for the values for what quantity under square root becomes negative, you've to exclude values x< -2, -8

Answer 10

x< = -2,-8

Answer 11

@Saeko did you get this?

Answer 12

its -2 because that gives sqrt(-8+8) = 0

Answer 13

smaller than? wouldn't it be larger than? since it can't be a negative value

Answer 14

oh i get it, except i'm sorta confused on the < or > part

Answer 15

yes...for larger values it'll be positive

Answer 16

so greater than?

Answer 17

no...only less than...cuz for values greater than 2 function will hold the definition and it will be positive

Answer 18

oooh...ok
thanks :)

Answer 19

:)