| Topic | Problem | Solution |
|---|---|---|
| None | \[ f(x)=x-3 \text { and } g(x)=x^{2}-2 \] Step 1 … | The formula for \((f \circ g)(x)\), also known as the composition of functions f and g, is given by… |
| None | One airplane is approaching an airport from the n… | Let's denote the distance of the northbound plane to the airport as \(x\), the distance of the east… |
| None | Find a formula for the inverse of the following f… | The function given is \(g(x)=(x-4)^{4}+4\), with the domain \(x \geq 4\). |
| None | \[ f(x)=|x| \text { and } g(x)=-4 x \] Step 2 of … | Define the functions f(x) = |x| and g(x) = -4x. |
| None | \[ f(x)=x^{2}-4 \text { and } g(x)=4 x \] Step 2 … | The function \(\left(\frac{f}{g}\right)(x)\) is the division of the function \(f(x)\) by the functi… |
| None | \[ f=\{(-1,1),(1,-2),(3,-4)\} \] and \[ g=\{(5,0)… | Given functions f and g as follows: |
| None | \[ f=\{(2,-2),(4,-3),(1,-2)\} \] and \[ g=\{(1,2)… | The function (f+g)(x) is defined as f(x) + g(x). So, to find (f+g)(1), we need to find the values o… |
| None | 8. A baseball team charges $\$ 30$ per ticket and… | Let's denote the drop in the ticket price from $30 as x. So, the ticket price is \(30 - x\) and the… |
| None | 12. Find a rational function $f(x)$ that meets th… | First, we need to find a function that meets the given conditions. The function must have a vertica… |
| None | 13. Comp-Tech is a new firm that designs a rectan… | The problem is asking for the dimensions of a rectangular compost container that has a minimal surf… |
| None | A number $x$ is rounded to 3 significant figures … | Find the range of values that would round to 3.69 when rounded to 3 significant figures: lower_boun… |
| None | \( \frac{-12}{4}+t \frac{31}{4} \) | \( \frac{-12}{4}+\frac{31}{4}t \) |
| None | Risk taking is an Important part of investing. In… | The problem is asking for the score that separates the bottom 5% of customers from the rest. This i… |
| None | Solve the following absolute value equation. If n… | The absolute value of a number is its distance from zero on the number line. Therefore, an absolute… |
| None | A whale shark measures $30 \mathrm{~m}$ long. Det… | Convert the actual length of the whale shark to centimeters: \(30 m = 3000 cm\) |
| None | Construct a polynomial function with the stated p… | A polynomial function of degree n with zeros r1, r2, ..., rn can be expressed in the form p(x) = a(… |
| None | Find the solution of the following polynomial ine… | We are given the polynomial inequality \(x(x+2)(x-3) \leq 0\). |
| None | The smallest gap between rims in the Grand Canyon… | Multiply the actual length of the gap by the scale factor: \(549 \times \frac{1}{90000} = 0.0061 \)… |
| None | 76. The greatest gap between rims in the Grand Ca… | Given the gap on the map in centimeters: gap_on_map = 2.9 cm |
| None | The demand, $D$, for a new rollerball pen is give… | Given the demand function $D=0.007 p^{3}-0.5 p^{2}+130 p$, where $p$ is the price in dollars. |
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