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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.)

Suppose H x V6x4Find two functions fand g such that f 9g x H xNeither function can be the identity functionThere may be more than one correct answer class=

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Solution.

Given

[tex]\begin{gathered} H(x)=\sqrt{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}[/tex][tex]\begin{gathered} Let\text{ g\lparen x\rparen=6x+4} \\ And\text{ f\lparen x\rparen = }\sqrt{x} \\ Thus, \\ (fog)(x)=\sqrt{g(x)}=\sqrt{6x+4} \end{gathered}[/tex]

Thus, the answer is

[tex]\begin{gathered} f(x)=\sqrt{x}\text{ and } \\ g(x)=6x+4 \end{gathered}[/tex]

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