Find (f∘g)(x).
f(x)=x–3
g(x)=2x2–5
Write your answer as a polynomial in simplest form.
(f∘g)(x)=
To find (f ∘ g)(x), we substitute g(x) into f(x). Therefore,
(f ∘ g)(x) = f(g(x)) = f(2x^2 - 5).
Now, substitute x - 3 into g.
(f ∘ g)(x) = f(2(x^2 - 3))
Next, distribute the 2.
(f ∘ g)(x) = f(2x^2 - 6)
Lastly, substitute x - 3 into f.
(f ∘ g)(x) = 2x^2 - 6 - 3
Simplifying, we get:
(f ∘ g)(x) = 2x^2 - 9
To find (f∘g)(x), we need to substitute g(x) into f(x) and simplify the expression.
Given:
f(x) = x - 3
g(x) = 2x^2 - 5
Substituting g(x) into f(x), we get:
(f∘g)(x) = f(g(x))
Substituting g(x) = 2x^2 - 5 into f(x), we have:
(f∘g)(x) = f(2x^2 - 5)
Now, substitute (2x^2 - 5) into x in f(x):
(f∘g)(x) = (2x^2 - 5) - 3
Simplifying the expression:
(f∘g)(x) = 2x^2 - 5 - 3
(f∘g)(x) = 2x^2 - 8
Therefore, (f∘g)(x) = 2x^2 - 8.
To find (f∘g)(x), we need to first evaluate g(x) and then substitute the result into f(x).
Let's find g(x) first:
g(x) = 2x^2 - 5
Now, substitute g(x) into f(x):
f(g(x)) = f(2x^2 - 5)
Next, replace x in f(x) with the expression 2x^2 - 5:
f(g(x)) = (2x^2 - 5) - 3
Simplify:
f(g(x)) = 2x^2 - 8
Therefore, (f∘g)(x) = 2x^2 - 8.