The Arithmetic of Functions is a concept in mathematics that involves the use of fundamental arithmetic operations such as addition, subtraction, multiplication, and division applied to functions. It also encompasses the composition of functions. This notion aids us in forming new functions and grasping intricate connections between variables within the realm of mathematics.
| Topic | Problem | Solution |
|---|---|---|
| None | Evaluate the function $h(x)=x^{4}-4 x^{2}+5$ at t… | First, we substitute the given values into the function \(h(x)=x^{4}-4 x^{2}+5\). |
| None | Given $f(x)=x-1$ and $g(x)=5 x^{2}$, first find $… | Given \(f(x)=x-1\) and \(g(x)=5 x^{2}\). We need to find the sum, difference, product, and quotient… |
| None | Find the formula for $(f \cdot g)(x)$. \[ f(x)=2 … | The formula for \((f \cdot g)(x)\), also known as the product of functions f and g, is given by \(f… |
| None | Evaluate $f(x)$ for the given values for $x$. The… | We are given the function \(f(x) = x^3 + 4\) and we need to find the value of \(f(x)\) when \(x = -… |
| None | 5. Evaluate $f(x)=2 x^{2}-3 x+2$ a. $f(-2)$ b. $f… | The function \(f(x)\) is given as \(2x^{2}-3x+2\). To find the value of the function at a specific … |
| None | Given the following function: \[ f(x)=6-8 x^{2} \… | Given the function \(f(x)=6-8 x^{2}\) |
| None | If $f(1)=1$ and $f(n)=f(n-1)+2$ then find the val… | Given that \(f(1)=1\) and \(f(n)=f(n-1)+2\) |
| None | Consider the following empty table for an arithme… | Define the arithmetic sequence as \(f(n)=12+9(n-1)\) and the geometric sequence as \(g(n)=64 \cdot\… |
| None | Find $f+g, f-g$, fg and $\frac{f}{g}$. Determine … | Let \(f(x)=2 x^{2}+5 x-18\) and \(g(x)=x-2\). We need to find the sum, difference, product, and quo… |
| None | - learn.hawkeslearning.com 노 凹 (1) Save \& Exit C… | The question asks to evaluate the function $f(x)=x^{3}+6 x-5$ for $x=-2$. To do this, we need to su… |
| None | 1. Let $f(x)=2 \sqrt{3 x+4}$. Find and simplify $… | Let's substitute the given values of x into the function $f(x)=2 \sqrt{3 x+4}$. |
| None | Suppose that the functions $r$ and $s$ are define… | Let the functions $r$ and $s$ be defined as $r(x)=x^{3}$ and $s(x)=3 x^{2}$ for all real numbers $x… |
| None | Given that $f(x)=x^{2}-6 x$ and $g(x)=x+4$, find … | Given that $f(x)=x^{2}-6 x$ and $g(x)=x+4$ |
| None | The functions $f$ and $g$ are defined as follows … | The functions $f$ and $g$ are defined as follows: $f(x)=5x+4$ and $g(x)=2x^{2}-3x$. |
| None | Suppose that the functions $f$ and $g$ are define… | Suppose that the functions $f$ and $g$ are defined for all real numbers $x$ as follows: $f(x)=x-5$ … |
| None | Let $f(x)=4 x^{2}-3 x$ and $g(x)=x^{2}-x+2$. Find… | Let \(f(x)=4 x^{2}-3 x\) and \(g(x)=x^{2}-x+2\). We need to find the sum, difference, product, and … |
| None | Let $f(x)=7 x+6$ and $g(x)=4-x^{2}$. Evaluate the… | Define the functions: \(f(x) = 7x + 6\) and \(g(x) = 4 - x^2\). |
| None | Evaluate the function at the given value of the v… | To find the value of the function at a specific point, we need to substitute the given value into t… |
| None | Given the functions below, find $f(x)+g(x)$ \[ \b… | Given the functions \(f(x)=2x+5\) and \(g(x)=x^{2}-3x+1\). |
| None | Given the functions below, find $(g+h)(1)$. \[ \b… | Given the functions \(g(x)=x^{2}+4+2x\) and \(h(x)=-3x+2\), we are asked to find the value of \((g+… |
| None | Consider the function $f(x)=-x^{2}+5$ Use it to f… | First, we need to understand the function $f(x)=-x^{2}+5$. This is a quadratic function, where $x$ … |
| None | Given the function $f(x)=x-2$, find the value of … | Given the function \(f(x)=x-2\), we need to find the value of \(f\left(-\frac{1}{2}\right)\). |
| None | Given the function $f(x)=6 x^{2}-3 x+1$. Calculat… | Given the function \(f(x)=6 x^{2}-3 x+1\). We need to substitute the given x values into the functi… |
| None | The function $f$ is defined as follows. \[ f(x)=\… | The function \(f(x)\) is defined as \(f(x)=\sqrt[3]{x}+3\). |
| None | Suppose that the functions $f$ and $g$ are define… | First, we write the expressions for $(f-g)(x)$ and $(f \cdot g)(x)$. |
| None | If $f(x)=4 x-3$, find the following value. \[ \fr… | Find the values of f(9), f(7), and f(3) using the given function f(x) = 4x - 3: |
| None | Given that \( f(x)=x+2, g(x)=-5 x \) and \( h(x)=… | \( h(x)=2 f(x-2)-3 g(x-3) \) |
| None | Given that \( f(x)=-2 x, g(x)=x-5 \) and \( h(x)=… | \( h(x) = 3 f(x-2) + g(x) \) |