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Given the function
f(x)=-(1)/(2)x+1, find the value of
f(-(2)/(3)) in simplest form.
Answer:

Given the function $f(x)=-\frac{1}{2} x+1$ , find the value of $f\left(-\frac{2}{3}\right)$ in simplest form. $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Given the function

f(x)=-\frac{1}{2} x+1

, find the value of

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

in simplest form.

\newline

Answer:

Substitute $x$ in function: Substitute the value of $x$ with $-\frac{2}{3}$ in the function $f(x)$ .
$f(x) = -\frac{1}{2}x + 1$
f\left(-\frac{\(2\)}{\(3\)}\right) = -\frac{\(1\)}{\(2\)}\cdot\left(-\frac{\(2\)}{\(3\)}\right) + \(1
Multiply constants: Multiply the constants $-\frac{1}{2}$ and $-\frac{2}{3}$ .
$f\left(-\frac{2}{3}\right) = \left(\frac{1}{2}\right)\left(\frac{2}{3}\right) + 1$
= $\frac{1\times 2}{2\times 3} + 1$
= $\frac{1}{3} + 1$
Add to get final result: Add $1$ to $\frac{1}{3}$ to get the final result. $\newline$ $f\left(-\frac{2}{3}\right) = \frac{1}{3} + 1$ $\newline$ $= \frac{1}{3} + \frac{3}{3}$ $\newline$ $= \frac{1 + 3}{3}$ $\newline$ $= \frac{4}{3}$

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