Given the function f(x)=x^(2)+3, find the value of f(-(2)/(3)) in simplest form. Answer:

Given Function: We are given the function f(x) = x^2 + 3 and we need to find the value of f(-(2/3)). First, we substitute x with -(2/3) in the function. f(-(2/3)) = (-(2/3))^2 + 3Substitution and Calculation: Now we calculate the square of -(2/3). (-(2/3))^2 = (-2/3) * (-2/3) = 4/9Calculate Square: Next, we add 3 to the result of the square of -(2/3). f(-(2/3)) = 4/9 + 3 To add 3 (which is the same as 27/9) to 4/9, we find a common denominator, which is already 9.Add 3: We add the two fractions. f(-(2/3)) = 4/9 + 27/9 = (4 + 27)/9 = 31/9Final Answer: We have found the value of f(-(2/3)) in simplest form. Therefore, the final answer is f(-(2/3)) = 31/9.

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Given the function
f(x)=x^(2)+3, find the value of
f(-(2)/(3)) in simplest form.
Answer:

Given the function $f(x)=x^{2}+3$ , find the value of $f\left(-\frac{2}{3}\right)$ in simplest form. $\newline$ Answer:

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Algebra 2

Find the vertex of the transformed function

Full solution

Q. Given the function

f(x)=x^{2}+3

, find the value of

f\left(-\frac{2}{3}\right)

in simplest form.

\newline

Answer:

Given Function: We are given the function $f(x) = x^2 + 3$ and we need to find the value of $f\left(-\left(\frac{2}{3}\right)\right)$ . First, we substitute $x$ with $-\left(\frac{2}{3}\right)$ in the function. $f\left(-\left(\frac{2}{3}\right)\right) = \left(-\left(\frac{2}{3}\right)\right)^2 + 3$
Substitution and Calculation: Now we calculate the square of $-\left(\frac{2}{3}\right)$ . $\newline$ $\left(-\left(\frac{2}{3}\right)\right)^2 = \left(-\frac{2}{3}\right) \times \left(-\frac{2}{3}\right) = \frac{4}{9}$
Calculate Square: Next, we add $3$ to the result of the square of $-(\frac{2}{3})$ . $\newline$ $f(-(\frac{2}{3})) = \frac{4}{9} + 3$ $\newline$ To add $3$ (which is the same as $\frac{27}{9}$ ) to $\frac{4}{9}$ , we find a common denominator, which is already $9$ .
Add $3$ : We add the two fractions. $\newline$ $f\left(-\frac{2}{3}\right) = \frac{4}{9} + \frac{27}{9} = \frac{4 + 27}{9} = \frac{31}{9}$
Final Answer: We have found the value of $f\left(-\frac{2}{3}\right)$ in simplest form. $\newline$ Therefore, the final answer is $f\left(-\frac{2}{3}\right) = \frac{31}{9}$ .