Find (f∘g)(x).
f(x)=x2
g(x)=
–
5x–3
Write your answer as a polynomial in simplest form.
(f∘g)(x)=
To find (f∘g)(x), we substitute g(x) into f(x) and simplify.
(g(x) = -5x - 3)
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(-5x - 3)
Substituting into f(x), we get:
(f∘g)(x) = (-5x - 3)^2
(f∘g)(x) = (-5x - 3)(-5x - 3)
(f∘g)(x) = 25x^2 + 15x + 15x + 9
(f∘g)(x) = 25x^2 + 30x + 9
Therefore, (f∘g)(x) = 25x^2 + 30x + 9.
To find (f∘g)(x), we substitute g(x) into f(x).
First, we substitute g(x) into f(x):
f(g(x)) = (g(x))^2
Now, substitute the expression for g(x) into f(x):
f(g(x)) = (–5x–3)^2
Expanding the expression, we get:
f(g(x)) = (-5x - 3)(-5x - 3)
Using the FOIL method to multiply the terms:
f(g(x)) = 25x^2 + 15x + 15x + 9
Combining like terms:
f(g(x)) = 25x^2 + 30x + 9
Therefore, (f∘g)(x) = 25x^2 + 30x + 9.
To find (f∘g)(x), we need to substitute the expression for g(x) into the function f(x) and simplify the resulting expression.
Given:
f(x) = x^2
g(x) = -5x - 3
Substituting g(x) into f(x), we have:
(f∘g)(x) = f(g(x))
= f(-5x - 3)
Now, replace x in f(x) with -5x - 3:
(f∘g)(x) = (-5x - 3)^2
To simplify this expression, we need to expand and simplify the square:
(f∘g)(x) = (-5x - 3)(-5x - 3)
= 25x^2 + 15x + 15x + 9
= 25x^2 + 30x + 9
Therefore, (f∘g)(x) = 25x^2 + 30x + 9.