Find functions \( f \) and \( g \) so that \( f \circ g=H \). \( H(x)=|2 x+7| \) Choose the correct pair of functions. A. \( f(x)=|x|, g(x)=2 x+7 \) B. \( f(x)=|-x|, g(x)=\frac{x-7}{2} \) C. \( f(x)=2 x+7, g(x)=|x| \) D. \( f(x)=\frac{x-7}{2}, g(x)=|-x| \)

The function \( f(x)=x^{3}-5 \) is one-to-one. (a) Find the inverse of \( f \) and check the answer. (b) Find the domain and the range of \( f \) and \( { }^{-1} \) (c) Graph \( f, f^{-1} \), and \( y=x \) on the same coordinate axes. (a) \( f^{-1}(x)=\sqrt[3]{x+5} \) (Simplify your answer. Use integers or fractions for any numbers in the expression.) (b) Find the domain of \( f \). Select the correct choice below and, if necessary, fill in the answer box to o B. The domain is \( \{x \mid x \neq \square \). C. The domain is \( \{x \mid x \leq\} \). D. The domain is the set of all real numbers. ( \( 4 x \mid x \geq\} \).

List the domain and the \( x \)-and \( y \)-intercepts of the following function. Graph the function. \( f(x)=\frac{5}{x} \)

Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and \( y \)-intercept of the function. \( f(x)=3+5^{x-1} \) Use the graphing tool to graph the function. (For any answer boxes shown with the grapher, type an exact answer.) What is the domain of \( f(x)=3+5^{x-1} \) ? ( \( -\infty, \infty \) ) (Type your answer in interval notation.) What is the range of \( f(x)=3+5^{x-1} ? \) \( \square \) (Type your answer in interval notation.)

Representar graficomente: a) \( f(x)=|x-1|+|x+2| \)

Begin with the graph of \( y=e^{x} \). Use transformations to graph the function below. Then determine its domain, range, and horizontal asymptote. \( f(x)=-8-e^{-x} \) Use the graphing tool to graph the function. (For any answer boxes shown with the grapher, type an exact answer.) What is the domain of \( f(x)=-8-e^{-x} \) ? (Type your answer in interval notation.)