Question

Given the definitions of f(a) and g(x) below, find the value of (19)( 1),f (x) = x2 + 3x – 11g(x) = 3a + 6

Answer 1

The given functions are,

`\begin{gathered} f(x)=x^2+3x-11_{} \\ g(x)=3x+6 \end{gathered}`

Fog can be determined as,

`\begin{gathered} \text{fog}=f(g(x)) \\ =f(3x+6) \\ =(3x+6)^2+3(3x+6)-11 \\ =9x^2+36+36x+9x+18-11 \\ =9x^2+45x+43 \end{gathered}`

The value of fog(-1) can be determined as,

`\begin{gathered} \text{fog}(-1)=9(-1)^2+45(-1)+43 \\ =9-45+43 \\ =7 \end{gathered}`

Thus, the requried value is 7.