Question

100 POINTS!!! VERY URGENT

Answer 1

D) (f o g)(x) = 10x² - 60x + 93

Explanation:

f(x) = 10x² + 3

g(x) = x - 3

⇒ (f o g)(x)

⇒ f(x - 3)

⇒ f(x - 3) = 10(x - 3)² + 3

⇒ f(x - 3) = 10(x² - 6x + 9) + 3

⇒ f(x - 3) = 10x² - 60x + 90 + 3

⇒ (f o g)(x) = 10x² - 60x + 93

Answer 2

`\textsf{D)} \quad (f \circ g)(x)=10x^2-60x+93`

Explanation:

`\textsf{If }\:f(x)=10x^2+3\:\textsf{ and }\:g(x)=x-3\:\textsf{ then}:`

`\begin{aligned}(f \circ g)(x) & = f[g(x)]\\ & = f(x-3)\\& = 10(x-3)^2+3\\& = 10(x^2-6x+9)+3\\& = 10x^2-60x+90+3\\& = 10x^2-60x+93\\\end{aligned}`