Find f X g , g X f , and f X f
f(x) = 3sqrt x-1 g(x) = x^3 + 1
For f(x) the 3 is little above the sqrt sign.
My answers were:
f(g(x)) = 3sqrt x^3 + 1 -1
g(f(x)) = 3sqrt (x-1)^3 -1
f(f) = 3sqrt x-1-1
My teacher said these were wrong. Please help. I do not know how to correct these. Thank you!
To find f(x) ⨉ g(x), g(x) ⨉ f(x), and f(x) ⨉ f(x), we need to substitute the respective functions into each other and simplify the expressions.
1. f(x) ⨉ g(x):
To find f(g(x)), we substitute g(x) into f(x) as follows:
f(g(x)) = 3√(g(x) - 1)
Now, substitute g(x) = x^3 + 1 into the above expression:
f(g(x)) = 3√((x^3 + 1) - 1) = 3√(x^3) = 3√x^3 = 3x^(3/2)
2. g(x) ⨉ f(x):
To find g(f(x)), we substitute f(x) into g(x) as follows:
g(f(x)) = (f(x))^3 + 1
Substitute f(x) = 3√(x - 1) into the above expression:
g(f(x)) = ((3√(x - 1))^3) + 1 = (3(x - 1)) + 1 = 3x - 2
3. f(x) ⨉ f(x):
To find f(f(x)), we substitute f(x) into f(x) as follows:
f(f(x)) = 3√(f(x) - 1)
Substitute f(x) = 3√(x - 1) into the above expression:
f(f(x)) = 3√(3√(x - 1) - 1)
These are the correct expressions for f(g(x)), g(f(x)), and f(f(x)).