Question

Graphs and Functions Expressing a function as a composition of two functions Suppose \( H(x)=\sqrt{7-2 x^{2}} \). Find two functions \( f \) and \( g \) such that \( (f \circ g)(x)=H(x) \). Neither function can be the identity function. (There may be more than one correct answer.) \[ \begin{array}{l} f(x)=\square \\ g(x)=\square \end{array} \]

          Graphs and Functions
Expressing a function as a composition of two functions
Suppose \( H(x)=\sqrt{7-2 x^{2}} \).
Find two functions \( f \) and \( g \) such that \( (f \circ g)(x)=H(x) \).
Neither function can be the identity function.
(There may be more than one correct answer.)
\[
\begin{array}{l}
f(x)=\square \\
g(x)=\square
\end{array}
\]

Graphs and Functions
Expressing a function as a composition of two functions
Suppose H(x)=√(7-2 x^2).
Find two functions f and g such that (f ∘ g)(x)=H(x).
Neither function can be the identity function.
(There may be more than one correct answer.)

f(x)=□

g(x)=□

Added by Luz M.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Dr Harish Viswanathan

Step 1

We need to express this function as a composition of two functions, \( f \) and \( g \), such that \( (f \circ g)(x) = H(x) \). Show more…

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Graphs and Functions Expressing a function as a composition of two functions Suppose \( H(x)=\sqrt{7-2 x^{2}} \). Find two functions \( f \) and \( g \) such that \( (f \circ g)(x)=H(x) \). Neither function can be the identity function. (There may be more than one correct answer.) \[ \begin{array}{l} f(x)=\square \\ g(x)=\square \end{array} \]