Question

Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers. F(X)=sqrt x+8, g(x)=x^2+3

Answer 1

Recall that:

`\begin{gathered} f(g(x))=f(x^2+3), \\ g(f(x))=g(√(x)+8). \end{gathered}`

Evaluating the functions, we get:

`\begin{gathered} f(g(x))=√(x^2+3)+8, \\ g(f(x))=(√(x)+8)^2+3. \end{gathered}`

Simplifying the second function, we get:

`g(f(x))=x+16√(x)+64+3=x+16√(x)+67.`

Answer:

`\begin{gathered} f(g(x))=√(x^2+3)+8, \\ g(f(x))=x+16√(x)+67. \end{gathered}`