2) Find f x g, g x f, and f x f
f(x) = 3sqrt x-1 g(x) = x^3+1
For the f(x) the 3 is little above the sqrt sign.
I do not understand how do find these.
To find f x g, g x f, and f x f, you need to understand function composition and apply it to the given functions f(x) = 3√(x - 1) and g(x) = x^3 + 1.
1) f x g:
To find f x g, you substitute g(x) into f(x) wherever you see the variable x in f(x). So, replacing x in f(x) with g(x), we get:
f x g = f(g(x)) = 3√(g(x) - 1)
Substitute g(x) = x^3 + 1 into the above expression:
f x g = 3√((x^3 + 1) - 1)
Simplifying further:
f x g = 3√(x^3) = 3|x|
2) g x f:
To find g x f, you substitute f(x) into g(x) wherever you see the variable x in g(x). So, replacing x in g(x) with f(x), we get:
g x f = g(f(x)) = (f(x))^3 + 1
Substitute f(x) = 3√(x - 1) into the above expression:
g x f = (3√(x - 1))^3 + 1
Simplifying further:
g x f = 27(x - 1) + 1 = 27x - 26
3) f x f:
To find f x f, you substitute f(x) into f(x) wherever you see the variable x in f(x). So, replacing x in f(x) with f(x), we get:
f x f = f(f(x)) = 3√(f(x) - 1)
Substitute f(x) = 3√(x - 1) into the above expression:
f x f = 3√(3√(x - 1) - 1)
Simplifying further may not be straightforward without additional context or constraints on the problem.
By following the steps of function composition, you can find the expressions for f x g, g x f, and f x f.