1. **State the problem:** We are given two functions: $$h(x) = x^2 - 7$$ $$f(x) = \frac{x}{5}$$ We need to find the compositions $$(h \circ f)(x)$$ and $$(f \circ h)(x)$$ and simplify them. 2. **Recall the definition of composition:** - $$(h \circ f)(x) = h(f(x))$$ means we substitute $f(x)$ into $h(x)$. - $$(f \circ h)(x) = f(h(x))$$ means we substitute $h(x)$ into $f(x)$. 3. **Find $$(h \circ f)(x)$$:** $$h(f(x)) = h\left(\frac{x}{5}\right) = \left(\frac{x}{5}\right)^2 - 7$$ Simplify the square: $$= \frac{x^2}{25} - 7$$ 4. **Find $$(f \circ h)(x)$$:** $$f(h(x)) = f(x^2 - 7) = \frac{x^2 - 7}{5}$$ 5. **Final answers:** $$(h \circ f)(x) = \frac{x^2}{25} - 7$$ $$(f \circ h)(x) = \frac{x^2 - 7}{5}$$ These are simplified expressions for the compositions.