Questions: Graphs and Functions Composition of a function with itself Suppose that the functions h and f are defined as follows. h(x) = 7 / (2x), x ≠ 0 f(x) = 6x - 9 Find the compositions h ∘ h and f ∘ f. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (h ∘ h)(x) = (f ∘ f)(x) =

Graphs and Functions Composition of a function with itself Suppose that the functions h and f are defined as follows. h(x) = 7 / (2x), x ≠ 0 f(x) = 6x - 9 Find the compositions h ∘ h and f ∘ f. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (h ∘ h)(x) = (f ∘ f)(x) =
Transcript text: https://www-awu.aleks.com/alekscgi/x/Isl.exe/10_u-IgNsIkr7j8P3jH-IQgKcWvCeq1apRdEMO8hKMyGpZKk8xhYw-s6... Graphs and Functions Composition of a function with itself Suppose that the functions $h$ and $f$ are defined as follows. \[ \begin{array}{l} h(x)=\frac{7}{2 x}, x \neq 0 \\ f(x)=6 x-9 \end{array} \] Find the compositions $h \circ h$ and $f \circ f$. Simplify your answers as much as possible. (Assume that your expressions are defined for all $x$ in the domain of the composition. You do not have to indicate the domain.) \[ \begin{array}{l} (h \circ h)(x)=\square! \\ (f \circ f)(x)=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Find \(f \circ f\)

Substitute \(f(x) = 7/(2_x)\) into itself in place of \(x\): \(f(f(x)) = 7/(2_(7/(2*x)))\) Simplify the expression: \(f \circ f = x\)

Step 2: Find \(g \circ g\)

Substitute \(g(x) = 6_x-9\) into itself in place of \(x\): \(g(g(x)) = 6_(6_x-9)-9\) Simplify the expression: \(g \circ g = 36_x - 63\)

Final Answer:

The composition \(f \circ f\) simplified is: \(f \circ f = x\) The composition \(g \circ g\) simplified is: \(g \circ g = 36*x - 63\)

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