Precálculo preguntas y respuestas

The range of the function \( f: f(x)=\frac{4-x^{2}}{x+2} \) is \( \ldots \ldots \ldots \) \( \begin{array}{llll}R-\{4\} & \text { b) } R-\{-2,2\} & \text { c) } R-\{-2,4\} & \text { d) } R^{+}-\{-2\end{array} \)

A water wheel has a radius of 21 feet. The wheel is rotating at 15 revolutions per minute. Find the linear speed, in feet per minute, of the water. The linear speed is approximately \( \square \) feet per minute. (Round to the nearest whole number as needed.)

1. The number of people in class decreases by multiplying by 0.95 each week. a) Are the output values increasing or decreasing? b) Is the pattern of change linear or exponential? c) If the pattern is linear, determine and interpret the constant rate of change. If the pattern is exponential, determine and interpret the percent increase/decrease. 2. The common ratio for the number of songs on your phone is 1.2 each month. a) Are the output values increasing or decreasing? b) Is the pattern of change linear or exponential? c) If the pattern is linear, determine and interpret the constant rate of change. If the pattern is exponential, determine and interpret the percent increase/decrease.

A water wheel has a radius of 17 feet. The wheel is rotating at 20 revolutions per minute. Find the linear speed, in feet per minute, of the water.

Convert \( \mathrm{r} \sqrt{1-5 \cos 2 \theta}=2 \) to carterian form.

The population of a particular city is increasing at a rate proportional to its size. It follows the function \( \mathrm{P}(\mathrm{t})=1+\mathrm{k} e^{0.09 \mathrm{t}} \) where k is a constant and t population is 23,000 , in how many years is the population expected to be 57,500 ? (Round to the nearest year.) A. 6 yr B. 10 yr C. 69 yr D. 4 yr

Find the domain and range of the inverse of the given function. \( f(x)=-\frac{4}{x} \) A. Domain and range: all real numbers B. Domain: \( (-\infty, 0) \cup(0, \infty) \); range: \( (-\infty, 0) \) D. Domain: all real numbers; range: \( (-\infty, 0) \cup(0, \infty) \) and range: \( (-\infty, 0) \cup(0, \infty) \)

Bentuk yang setara dengan \( \left(\mathrm{fog}^{-1}\right)^{-1}(x) \) adalah \( \begin{array}{ll}\text { (A) }\left(f^{-1} \circ g\right)(x) & \text { (D) }(g \circ)^{-1}(x) \\ \text { (B) }\left(g \circ f^{-1}\right)(x) & \text { (E) }\left(f^{-1}\right)(x) \\ \text { (C) }(f \circ g)^{-1}(x) & \end{array} \)

\( 1 \leftarrow \) Determine whether the function is one-to-one by graphing and using the horizontal line test. \( \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}-10}{\mathrm{x}+4} \)

एक जनसंख्या की वृद्धि खड़ा बारह महीने में दोगुनी होती है। यदि प्रारंभिक जनसंख्या 5000 हो, तो 3 वर्ष बाद जनसंख्या अनुमानित कितनी होगी?