Let f(x)= 2/3x^2-3/2x+5/7 and G(x)=1/3x-2/5.
(fg)(x)
To find (f ∘ g)(x), which means the composition of the functions f(x) and g(x), follow these steps:
Step 1: Start with the function g(x) and substitute it into f(x).
(f ∘ g)(x) = f(g(x))
Step 2: Replace every occurrence of x in f(x) with g(x).
f(g(x)) = 2/3(g(x))^2 - 3/2(g(x)) + 5/7
Step 3: Replace g(x) with its expression.
f(g(x)) = 2/3(1/3x - 2/5)^2 - 3/2(1/3x - 2/5) + 5/7
Step 4: Simplify and expand the expression.
f(g(x)) = 2/3(1/9x^2 - 4/15x + 4/25) - 1/2x + 1/5 + 5/7
Step 5: Distribute the fraction through the expression.
f(g(x)) = 2/27x^2 - 8/45x + 8/75 - 1/2x + 1/5 + 5/7
Step 6: Combine like terms.
f(g(x)) = 2/27x^2 - 8/45x - 11/75 + 5/7
So, (f ∘ g)(x) = 2/27x^2 - 8/45x - 11/75 + 5/7.