Find (f+g)(x),(f-g)(x),(f*g)(x), and (f/g)(x) for each f(x) and g(x)
Now we were working well on this until we got to this f(x) and g(x). This was something our teacher didn't bring up.
f(x) = 8x^2
g(x) = 1/x^2
How would you go about solving the problem with the fraction as g(x)? I just need explaining on the steps of working with the fraction, then I'll be able to work it out. No answers please.
(f+g)(x) = 8 x^2 + 1/x^2
(f-g)(x) = 8 x^2 - 1/x^2
f [g(x)] = f (1/x^2) = 8(1/x^4) = 8/x^4
f [1/g(x)] = f (x^2) = 8 x^4
Thank you for the help! I understand the concept of it now!
To find (f+g)(x), (f-g)(x), (f*g)(x), and (f/g)(x) for the given functions f(x) = 8x^2 and g(x) = 1/x^2, we can apply the appropriate operations to the functions.
1. (f+g)(x):
To find (f+g)(x), we need to add f(x) and g(x). This can be done by adding the functions together element-wise.
(f+g)(x) = f(x) + g(x) = 8x^2 + 1/x^2
2. (f-g)(x):
To find (f-g)(x), we need to subtract g(x) from f(x). This can be done by subtracting the functions element-wise.
(f-g)(x) = f(x) - g(x) = 8x^2 - 1/x^2
3. (f*g)(x):
To find (f*g)(x), we need to multiply f(x) and g(x) together.
(f*g)(x) = f(x) * g(x) = 8x^2 * 1/x^2 = 8
4. (f/g)(x):
To find (f/g)(x), we need to divide f(x) by g(x). When dividing by a fraction, we can multiply by its reciprocal.
(f/g)(x) = f(x) / g(x) = 8x^2 / (1/x^2)
To divide by a fraction, we can multiply by the reciprocal of that fraction. The reciprocal of 1/x^2 is x^2/1 = x^2.
(f/g)(x) = 8x^2 * (x^2/1) = 8x^4
So, the expressions for (f+g)(x), (f-g)(x), (f*g)(x), and (f/g)(x) for the given functions are:
(f+g)(x) = 8x^2 + 1/x^2
(f-g)(x) = 8x^2 - 1/x^2
(f*g)(x) = 8
(f/g)(x) = 8x^4