Given the function f(x)=-2x^(3)+(7)/(4)x, find the value of f((3)/(2)) in simplest form. Answer:

Substitute x into function: Substitute the value of x into the function. We are given f(x) = -2x^(3) + (7/4)x and we need to find f((3/2)). Let's substitute x = (3/2) into the function. f((3/2)) = -2(3/2)^(3) + (7/4)(3/2)Calculate cube of (3/2): Calculate the cube of (3/2). (3/2)^(3) = (3/2) * (3/2) * (3/2) = 27/8Multiply by -2: Multiply the result by -2. -2 * (27/8) = -54/8Simplify fraction -54/8: Simplify the fraction -54/8. -54/8 can be simplified by dividing both the numerator and the denominator by 2. -54/8 = -27/4Multiply (7/4) by (3/2): Multiply (7/4) by (3/2). (7/4) * (3/2) = 21/8Add results: Add the two results together. f((3/2)) = -27/4 + 21/8 To add these two fractions, we need a common denominator. The common denominator for 4 and 8 is 8.Convert -27/4 to fraction: Convert -27/4 to a fraction with a denominator of 8. -27/4 = -27/4 * (2/2) = -54/8Add fractions: Add the fractions with the common denominator. f((3/2)) = -54/8 + 21/8 f((3/2)) = (-54 + 21)/8 f((3/2)) = -33/8

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Given the function
f(x)=-2x^(3)+(7)/(4)x, find the value of
f((3)/(2)) in simplest form.
Answer:

Given the function $f(x)=-2 x^{3}+\frac{7}{4} x$ , find the value of $f\left(\frac{3}{2}\right)$ in simplest form. $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

Full solution

Q. Given the function

f(x)=-2 x^{3}+\frac{7}{4} x

, find the value of

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

in simplest form.

\newline

Answer:

Substitute $x$ into function: Substitute the value of $x$ into the function. $\newline$ We are given $f(x) = -2x^{3} + \frac{7}{4}x$ and we need to find $f\left(\frac{3}{2}\right)$ . Let's substitute $x = \frac{3}{2}$ into the function. $\newline$ $f\left(\frac{3}{2}\right) = -2\left(\frac{3}{2}\right)^{3} + \left(\frac{7}{4}\right)\left(\frac{3}{2}\right)$
Calculate cube of $(\frac{3}{2})$ : Calculate the cube of $(\frac{3}{2})$ . $(\frac{3}{2})^{3} = (\frac{3}{2}) \times (\frac{3}{2}) \times (\frac{3}{2}) = \frac{27}{8}$
Multiply by $-2$ : Multiply the result by -2＂).$\newline\$-2 \times \left(\frac{27}{8}\right) = -\frac{54}{8}$
Simplify fraction $-\frac{54}{8}$: Simplify the fraction $-\frac{54}{8}$.$-\frac{54}{8}$ can be simplified by dividing both the numerator and the denominator by $2$.$-\frac{54}{8} = -\frac{27}{4}$
Multiply $(\frac{7}{4})$ by $(\frac{\(3$}{$2$}): Multiply $(\frac{7}{4})$ by $(\frac{3}{2}).\(\newline$\$(\frac{7}{4}) \times (\frac{3}{2}) = \frac{21}{8}\)
Add results: Add the two results together.$\newline$$f\left(\frac{3}{2}\right) = -\frac{27}{4} + \frac{21}{8}$$\newline$To add these two fractions, we need a common denominator. The common denominator for $4$ and $8$ is $8$.
Convert $-\frac{27}{4}$ to fraction: Convert $-\frac{27}{4}$ to a fraction with a denominator of $8$.$-\frac{27}{4} = -\frac{27}{4} \times \frac{2}{2} = -\frac{54}{8}$
Add fractions: Add the fractions with the common denominator.$\newline$$f\left(\frac{3}{2}\right) = -\frac{54}{8} + \frac{21}{8}$$\newline$$f\left(\frac{3}{2}\right) = \frac{-54 + 21}{8}$$\newline$$f\left(\frac{3}{2}\right) = -\frac{33}{8}$