nswer:
[tex](f\circ g)(x)\text{ = 4x}^2+26x+29[/tex]
Explanation:
ere, we want to solve the given composuite function
What we have to do is to replace the x in f(x) with the entirety of g(x)
We have that as:
[tex]\begin{gathered} (f\circ\text{ g\rparen\lparen x\rparen = f\lparen g\lparen x\rparen\rparen} \\ =\text{ f\lparen2x+9\rparen} \end{gathered}[/tex]
Now, we replace x in f(x) with 2x+9 as stated
We have that as:
[tex]\begin{gathered} f(2x+9)\text{ = \lparen2x+9\rparen}^2-5(2x+9)\text{ - 7} \\ f(2x+9)\text{ = 4x}^2+36x+81-10x-45-7 \\ f(2x+9)\text{ = 4x}^2+36x-10x+81-45-7 \\ f(2x+9)\text{ = 4x}^2+26x+29 \end{gathered}[/tex]
