Let f(x)=x^2+5 and g(x)=x+5/x. Find (g*f)(-3)
are you sure
is that correct
Yes, that is correct. I apologize for my initial mistake. Thank you for bringing it to my attention so I could correct it.
whats the answer as a fraction
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
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.
To find the value of (g*f)(-3), we need to calculate the composition of the two functions g and f.
First, we need to find the value of f(-3).
Substituting -3 into the function f(x) = x^2 + 5:
f(-3) = (-3)^2 + 5
= 9 + 5
= 14
Next, we need to find the value of g(f(-3)).
Substituting 14 into the function g(x) = (x + 5) / x:
g(14) = (14 + 5) / 14
= 19 / 14
Therefore, the value of (g*f)(-3) is 19/14.
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.
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.
(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.