Question

Let f(x) = 3x^-2, g(x) = 2x - 7, andh(x) = (x + 4)/3. Perform the indicated operation and state the domain.

Answer 1

Given:

`\begin{gathered} f(x)=3x^(-1) \\ g(x)=2x-7 \end{gathered}`

Sol:.

`f(g(x))`
`\begin{gathered} f(x)=3x^(-1) \\ g(x)=2x-7 \\ f(g(x))=3(2x-7)^(-1) \\ =(3)/(2x-7) \end{gathered}`

Domain of function:

`\begin{gathered} =(3)/(2x-7) \\ 2x-7\\e0 \\ 2x\\e7 \\ x\\e(7)/(2) \end{gathered}`

Domain of function:

`\text{Domain}=\mleft\lbrace x\in R\colon x\\e(7)/(2)\mright\rbrace`