What is the composite function of

3x^2-5x+6 and x^2+3x and what is its domain and range

3 answers

the answer depends on the composition. If

f(x) = 3x^2+5x+6
g(x) = x^2+3x

then

(f◦g)(x) = f(g(x))
= 3g^2-5g+6
= 3(x^2+3x)^2 - 5(x^2+3x) + 6
= 3x^4 + 18x^3 + 22x^2 - 15x + 6

(g◦f)(x) = g(f(x))
= f^2+3f
= (3x^2-5x+6)^2 + 3(3x^2-5x+6)
= 9x^4 - 30x^3 + 70x^2 - 75x + 54

In either case, the domain is all reals.

Since they are 4th-degree polynomials, they will have a minimum value. Finding that may not be easy, but the range will be (minval,+∞)
How about this idk if im right for this part

F(x)=2^x g(x)=y-x
Edit for g(x) i mean g(x)=3-x