Arithmetic of Functions Introduction,Examples with Step-by-Step Explanations

The problems about Arithmetic of Functions

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 $2 x^{2} - 3 x + 2$ . 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: $f (x) = 5 x + 4$ and $g (x) = 2 x^{2} - 3 x$ .
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: $f (x) = 7 x + 6$ 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 $f (x) = 2 x + 5$ and $g (x) = x^{2} - 3 x + 1$ .
None	Given the functions below, find $(g + h) (1)$ . \[ \b…	Given the functions $g (x) = x^{2} + 4 + 2 x$ and $h (x) = - 3 x + 2$ , 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 $f (- \frac{1}{2})$ .
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)=…	$h (x) = 3 f (x - 2) + g (x)$