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

Substitute x: Substitute x with -(1/2) in the function f(x) = 2x^2 - 3x^3. f(-(1/2)) = 2(-1/2)^2 - 3(-1/2)^3Calculate square and cube: Calculate the square and cube of -(1/2). (-1/2)^2 = (1/4) and (-1/2)^3 = -(1/8)Replace exponents in function: Replace the exponents in the function with their calculated values. f(-(1/2)) = 2(1/4) - 3(-1/8)Multiply coefficients by exponents: Multiply the coefficients by the calculated exponents. f(-(1/2)) = (2/1)*(1/4) - (3/1)*(-1/8) f(-(1/2)) = 1/2 - (-3/8)Simplify expression: Simplify the expression by adding the fractions. f(-(1/2)) = 1/2 + 3/8 To add these fractions, find a common denominator.Find common denominator: The common denominator for 2 and 8 is 8. Convert 1/2 to a fraction with a denominator of 8. 1/2 = 4/8Convert 1/2 to fraction: Add the fractions with the common denominator. f(-(1/2)) = 4/8 + 3/8 f(-(1/2)) = 7/8

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

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given the function

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

, find the value of

f\left(-\frac{1}{2}\right)

in simplest form.

\newline

Answer:

Substitute $x$ : Substitute $x$ with $-\left(\frac{1}{2}\right)$ in the function $f(x) = 2x^2 - 3x^3.$ $\newline$ f\left(-\left(\frac{$1$}{$2$}\right)\right) = \(2\left(-\frac{ $1$ }{ $2$ }\right)^ $2$ - $3$ \left(-\frac{ $1$ }{ $2$ }\right)^ $3$
Calculate square and cube: Calculate the square and cube of $-(1/2)$ . $(-1/2)^2 = (1/4)$ and $(-1/2)^3 = -(1/8)$
Replace exponents in function: Replace the exponents in the function with their calculated values. $\newline$ $f(-\frac{1}{2}) = 2(\frac{1}{4}) - 3(-\frac{1}{8})$
Multiply coefficients by exponents: Multiply the coefficients by the calculated exponents. $\newline$ $f\left(-\frac{1}{2}\right) = \frac{2}{1}\cdot\frac{1}{4} - \frac{3}{1}\cdot\left(-\frac{1}{8}\right)$ $\newline$ $f\left(-\frac{1}{2}\right) = \frac{1}{2} - \left(-\frac{3}{8}\right)$
Simplify expression: Simplify the expression by adding the fractions. $\newline$ $f(-\frac{1}{2}) = \frac{1}{2} + \frac{3}{8}$ $\newline$ To add these fractions, find a common denominator.
Find common denominator: The common denominator for $2$ and $8$ is $8$ . $\newline$ Convert $\frac{1}{2}$ to a fraction with a denominator of $8$ . $\newline$ $\frac{1}{2} = \frac{4}{8}$
Convert $\frac{1}{2}$ to fraction: Add the fractions with the common denominator. $\newline$ $f\left(-\left(\frac{1}{2}\right)\right) = \frac{4}{8} + \frac{3}{8}$ $\newline$ $f\left(-\left(\frac{1}{2}\right)\right) = \frac{7}{8}$