Question

Suppose H (x) = V6x+4.Find two functions fand g such that (f 9g) (x) = H (x).Neither function can be the identity function.(There may be more than one correct answer.)

Answer 1

Solution.

Given

`\begin{gathered} H(x)=√(6x+4) \\ We\text{ want to find two functions f and g such that \lparen fog\rparen\lparen x\rparen=H\lparen x\rparen} \\ \end{gathered}`
`\begin{gathered} Let\text{ g\lparen x\rparen=6x+4} \\ And\text{ f\lparen x\rparen = }√(x) \\ Thus, \\ (fog)(x)=√(g(x))=√(6x+4) \end{gathered}`

Thus, the answer is

`\begin{gathered} f(x)=√(x)\text{ and } \\ g(x)=6x+4 \end{gathered}`