Answer:
D) (f o g)(x) = 10x² - 60x + 93
Step-by-step 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
[tex]\textsf{D)} \quad (f \circ g)(x)=10x^2-60x+93[/tex]
[tex]\textsf{If }\:f(x)=10x^2+3\:\textsf{ and }\:g(x)=x-3\:\textsf{ then}:[/tex]
[tex]\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}[/tex]
