♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]f(x) = 2 {x}^{2} - 7x - 7[/tex]
[tex]g(x) = x + 1[/tex]
_________________________________
[tex]f(g(x)) = 2 ({x + 1})^{2} - 7(x + 1) - 7 \\ [/tex]
[tex]f(g(x)) = 2( {x}^{2} + 2x + 1) - 7x - 7 - 7 \\ [/tex]
[tex]f(g(x)) = 2 {x}^{2} + 4x + 2 - 7x - 7 - 7 \\ [/tex]
Collect like terms
[tex]f(g(x)) = 2 {x}^{2} + (4 - 7)x - 14 + 2 \\ [/tex]
[tex]f(g(x)) = 2 {x}^{2} - 3x - 12 [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
[tex]2x^{2} -3x-12[/tex]
Step-by-step explanation:
To solve composite functions, figure out which function is on the "inside" and the outside":
f(x) is the inside and g(x) is the outside
Now plug the value of g(x) into the x values of f(x):
[tex]2(x+1)^{2}-7(x+1)-7[/tex]
Then distribute following the steps of PEMDAS:
[tex]2(x^{2}+2x+1)-7x-7-7[/tex]
[tex]2x^{2} + 4x + 2 - 7x -14[/tex]
Then combine like terms:
[tex]2x^{2} -3x-12[/tex]
