Question

what is x^2 times radical(x+3)? and what is the domain?

Answer 1

The expression that will restrict the domain is \[\large \sqrt{x+3}\] since you cannot take the square root of a negative number. So \[\large x+3\ge0\] which means that \[\large x\ge-3\]

Answer 2

your radical needs to be indexed it youre going to write it like that

Answer 3

is it possible to solve for x in this equation?

Answer 4

you mean in the original expression or the inequality I just wrote out?

Answer 5

original expression

Answer 6

no you cannot solve for x in the original expression because there is no equal sign or inequality sign

Answer 7

well the full question started with (h*g)(x)=___? and h=x^2 and g=radical x+3

Answer 8

??

Answer 9

is that h times g or is that h composes g?

Answer 10

it is a circle in the question so i assume it is multiplication?

Answer 11

okay its multiplication yes

Answer 12

so it really looks like this

\[\large (h\circ g)(x)\]

???

Answer 13

yesss

Answer 14

ok thx

Answer 15

\[\large (h\circ g)(x)\] really means \[\large h(g(x))\], ie \[\large (h\circ g)(x)=h(g(x))\]

Answer 16

ohh

Answer 17

So start with h(x) and replace every x with g(x) to go from



h(x)=x^2



to


h(g(x))=(g(x))^2



Now replace g(x) in the right side to with sqrt(x+3) to get



h(g(x))=(sqrt(x+3))^2


and now square the square root so it cancels out to give us


h(g(x))=x+3


Note: this is assuming that x is nonnegative.

Answer 18

-3 isnt the answer i tried on the website im doing this on

Answer 19

oh wait the equation is the answer?

Answer 20

got it!

Answer 21

yes, \[\large (h\circ g)(x)=x+3\] where x is assumed to be nonnegative