Question

If g(x) = sqrt(x-3) and k(x) = x^2 + 5 then determine (kg)(x).

Answer 1

(k-g)(5) means plug 5 into both equations, then divide the answer of k(x) by g(x)
(g o k)(7) means plug 7 the equation k(x) and then plug the answer you get from k(x) into g(x)

Answer 2

(k - g)(5) =(x²+5)–x–3
= x²-x+2 = 5²-5+2
= 22

Answer 3

\[(kg)(x)=(x^2+5)(\sqrt{x ^{-3})}\]

Answer 4

hope it helps

Answer 5

Where did you get (k-g) @rhr12? It says to multiply k and g. Were you just giving an example?

Answer 6

I agree with saseal that \[(kg)(x) = k(x)g(x) = (x^2+5)\sqrt{x-3}\]

Answer 7

So what would you plug in for x?

Answer 8

Or would you have to multiply that first?

Answer 9

\[\sqrt{x-3}=(x-3)^{\frac{ 1 }{ 2 }}\]

Answer 10

theres nothing to plug in, theres no value given in the question

Answer 11

So I have to multiply it....Couldn't I just square both equations to get rid of the square root?

Answer 12

i dont think you can multiply, just leave it that way

Answer 13

I don't know think I'd bother multiplying it out, if its actually possible. If I wanted to evaluate (kg) at say x=10, I'd just use it as a normal function and substitute x = 10 everywhere. i.e.\[(kg)(10) = (10^2+5)\sqrt{10-7} = 105\sqrt{7}\]

Answer 14

So just write (x^2 + 5)(sqrt(x - 3))?

Answer 15

yea

Answer 16

It should be \[\sqrt{10-3} \text{ instead of } \sqrt{10-7}\]
and yep that is what I'd write

Answer 17

Alright thanks!