SOLUTION: for the indicated functions f and g, find the functions f°g ,and g°f, and find their domains. f(x)= x^3; g(x)= x^2 - x + 1

Algebra ->  Functions -> SOLUTION: for the indicated functions f and g, find the functions f°g ,and g°f, and find their domains. f(x)= x^3; g(x)= x^2 - x + 1      Log On


   

Question 940032: for the indicated functions f and g, find the functions f°g ,and g°f, and find their domains.
f(x)= x^3; g(x)= x^2 - x + 1
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=+x%5E3
+g%28x%29+=x%5E2-x%2B1
fog = f(g(x))
=+f%28x%5E2-x%2B1%29
replace x with (x^2-x+1)
=+%28x%5E2-x%2B1%29%5E3
fog =%28x%5E2-x%2B1%29%5E3
domain: for all values of x, the above function is valid
hence domain = all real numbers(R)
gof = g(f(x))
=g(x^3)
replace x with x^3
= %28x%5E3%29%5E2-x%5E3%2B1
=X%5E6-X%5E3%2B1
domain: for all values of x, the above function is valid
hence domain = all real numbers(R)