Find (f∘g)(x).
f(x)=x2
g(x)=x+5
Write your answer as a polynomial in simplest form.
(f∘g)(x)=
(f∘g)(x) = f(g(x))
= f(x+5)
= (x+5)^2
= x^2 + 10x + 25
To find (f∘g)(x), we first need to substitute the function g(x) into f(x).
Given:
f(x) = x^2
g(x) = x + 5
Substituting g(x) into f(x):
(f∘g)(x) = f(g(x))
= f(x + 5)
Now, substitute x + 5 into f(x):
(f∘g)(x) = (x + 5)^2
Expanding the squared term:
(f∘g)(x) = (x + 5)(x + 5)
= x(x + 5) + 5(x + 5)
= x^2 + 5x + 5x + 25
= x^2 + 10x + 25
Therefore, (f∘g)(x) = x^2 + 10x + 25.
To find (f∘g)(x), we need to substitute g(x) into f(x).
First, let's find g(x):
g(x) = x + 5
Now, substitute g(x) into f(x):
f(g(x)) = (x + 5)^2
Expanding (x + 5)^2:
f(g(x)) = x^2 + 2*5*x + 5^2
Simplifying:
f(g(x)) = x^2 + 10x + 25
Therefore, the polynomial in simplest form for (f∘g)(x) is:
(f∘g)(x) = x^2 + 10x + 25