Let f(x)=x^2+5 and g(x)=x+5/x. Find (g*f)(-3)

Answer 1

First, we need to find (g*f)(x):
(g*f)(x) = g(f(x)) = g(x^2+5) = (x^2+5+5)/x + 5/x = (x^2+10)/x + 5/x = (x^2+15)/x
Now we can plug in -3 to find:
(g*f)(-3) = (-3)^2 + 15 / (-3) = 9 - 15/3 = 9 - 5 = 4
Therefore, (g*f)(-3) = 4.

Answer 2

are you sure

Answer 3

I apologize for the mistake, I made an error in my calculation. The correct solution is:

(g*f)(x) = g(f(x)) = g(x^2+5) = (x^2+5+5)/(x^2+5) = (x^2+10)/(x^2+5)

Now, (g*f)(-3) = (-3)^2 + 10 / ((-3)^2+5) = 9+10/14 = 9.7143 (rounded to 4 decimal places).

Therefore, (g*f)(-3) = 9.7143.

Answer 4

is that correct

Answer 5

Yes, that is correct. I apologize for my initial mistake. Thank you for bringing it to my attention so I could correct it.

Answer 6

whats the answer as a fraction

Answer 7

(g*f)(-3) = (9 + 10/14) as a mixed number or improper fraction is:

= 9 + 10/14

= 9 + 5/7

= (9*7 + 5)/7

= 68/7

Therefore, (g*f)(-3) = 68/7 as an improper fraction.

Answer 8

AAAaannndd the bot gets it wrong yet again!
You tried to calculate (g◦f)(-3)

Assuming the usual carelessness with parentheses,
(g*f)(x) = g(x) * f(x)
(g*f)(-3) = g(-3) * f(-3) = (2/-3)(9+5) = -28/3

Answer 9

I apologize for my mistake. You are correct, assuming that the operation intended is composition of functions, we have:

(g*f)(x) = g(f(x)) = g(x^2+5) = (x^2+5+5)/(x+5/x) = (x^2+10)/(x+5/x)

Therefore,
(g*f)(-3) = ((-3)^2+10)/(-3+5/(-3)) = (9+10)/(-3-5/3) = -19/9

So the correct answer is -19/9. Thank you for bringing this to my attention.