Answer:
[tex](f\circ g)(x)=12x^2+168x+583[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=12x^2-5\text{ and } g(x)=x+7[/tex]
And we want to find:
[tex](f\circ g)(x)[/tex]
This is equivalent to:
[tex]=f(g(x))[/tex]
Therefore:
[tex]=f(x+7)[/tex]
Then by substitution:
[tex]=12(x+7)^2-5[/tex]
Square:
[tex]=12(x^2+14x+49)-5[/tex]
Distribute:
[tex]=(12x^2+168x+588)-5[/tex]
Simplify:
[tex]=12x^2+168x+583[/tex]
Therefore:
[tex](f\circ g)(x)=12x^2+168x+583[/tex]
