Final answer:
To find (f.g)(x), substitute the function g(x) into the function f(x) and simplify the expression.(f.g)(x) = 49/(x^2*2) - 32/sqrt(2) - 49/(x*sqrt(2)) + 300 - 4sqrt(2)
Step-by-step explanation:
To find (f.g)(x), we need to substitute the function g(x) into the function f(x). First, let's substitute g(x) into f(x):
f(g(x)) = (g(x))^2 - 7(g(x)) + 12
Now, substitute the values of g(x) into this expression:
f(g(x)) = (7/xsqrt(2) - 16)^2 - 7(7/xsqrt(2) - 16) + 12
Next, simplify this expression:
f(g(x)) = (49/(x^2*2) - 32/sqrt(2) + 256) - (49/ (x*sqrt(2)) - 112 + 16) + 12
Finally, combine like terms and simplify the expression:
f(g(x)) = 49/(x^2*2) - 32/sqrt(2) + 256 - 49/(x*sqrt(2)) + 112 - 16 + 12
The final expression for (f.g)(x) is:
(f.g)(x) = 49/(x^2*2) - 32/sqrt(2) - 49/(x*sqrt(2)) + 300 - 4sqrt(2)