Answer:
We get [tex]\mathbf{(fog)(x)=x^3+12x^2+21x-98}[/tex]
Step-by-step explanation:
We are given:
[tex]f(x) = x^2 + 5x - 14 \\ g(x) = x + 7[/tex]
We need to find [tex](f o g)(x)[/tex]
We know that: [tex](fog)(x)=f(x)\times g(x)[/tex]
We multiply the both terms i.e. f(x) and g(x) to get our answer.
[tex](fog)(x)\\=f(x)\times g(x)\\=(x^2+5x-14)(x+7)\\=(x^2+5x-14)(x)+(x^2+5x-14)(7)\\=x^3+5x^2-14x+7x^2+35x-98\\Combining\:like\:terms:\\=x^3+5x^2+7x^2-14x+35x-105\\=x^3+12x^2+21x-98[/tex]
So, we get [tex]\mathbf{(fog)(x)=x^3+12x^2+21x-98}[/tex]
