Pair of functions fx=3x and g(x) =3x^2-2x+3 find the following (f◦g)(x=)
(f◦g)(x)
f(x) = 3x
f(g) = 3g
but, g = 3x^2-2x+3
so, f(g) = 3(3x)^2 - 2(3x) + 3 = 9x^2 - 6x + 3
similarly, for (g◦f)(x)
g(f) = 3f^2 - 2f + 3
= 3(3x)^2 - 2(3x) + 3 = 27x^2 - 6x + 3
strange typo, but correct answer
f(g) = 3(3x^2 - 2x + 3) = 9x^2 - 6x + 3
To find (f◦g)(x), we need to substitute g(x) into the function f(x). In other words, we need to replace every occurrence of x in f(x) with g(x).
The function f(x) is given as fx = 3x.
The function g(x) is given as g(x) = 3x^2 - 2x + 3.
To find (f◦g)(x), we substitute g(x) into f(x). So, we replace every occurrence of x in f(x) with g(x) as follows:
(f◦g)(x) = f(g(x))
= f(3x^2 - 2x + 3)
Now, we substitute 3x^2 - 2x + 3 into f(x):
(f◦g)(x) = 3(3x^2 - 2x + 3)
Simplifying further:
(f◦g)(x) = 9x^2 - 6x + 9
Therefore, (f◦g)(x) is equal to 9x^2 - 6x + 9.