Question

Let F(x)=3x-1 and g(x)=×+2. Findf(g(x)) and g(f(x))

Answer 1

Given:

`\begin{gathered} f(x)=3x-1 \\ g(x)=x+2 \end{gathered}`

To find f(g(x)):

`\begin{gathered} f(g(x))\text{ means substitute g\lparen x\rparen into f\lparen x\rparen} \\ f(g(x))=3(x+2)-1 \\ f(g(x))=3x+6-1 \\ f(g(x))=3x+5 \end{gathered}`

Therefore, f(g(x)) = 3x + 5

To find g(f(x)):

`\begin{gathered} g(f(x))\text{ means substitute f\lparen x\rparen into g\lparen x\rparen} \\ g(f(x))=(3x-1)+2 \\ g(f(x))=3x-1+2 \\ g(f(x))=3x+1 \end{gathered}`

Therefore, g(f(x)) = 3x + 1