Given the function f(x)=2x^(2)+1, find the value of f(-(5)/(2)) in simplest form. Answer:

Substitute x in function: Substitute the value of x into the function. We are given f(x) = 2x^2 + 1 and we need to find f(-(5/2)). So we will substitute x with -(5/2) in the function. f(-(5/2)) = 2(-(5/2))^2 + 1Simplify negative square: Simplify the exponent. We need to square -(5/2). Remember that when you square a negative number, the result is positive. (-(5/2))^2 = (-5/2) * (-5/2) = 25/4Multiply by 2: Multiply the result by 2. Now we multiply the squared value by 2 as per the function. 2 * (25/4) = 50/4Simplify function: Simplify the function. We now have all the parts to simplify the function. f(-(5/2)) = 50/4 + 1Convert constant to common denominator: Convert the constant term to have a common denominator with the fraction. To add the fraction and the constant term, we need a common denominator. The number 1 can be written as 4/4. 1 = 4/4Add fraction and constant: Add the fraction and the constant term. Now we add the two terms together. 50/4 + 4/4 = 54/4Simplify final fraction: Simplify the fraction. The fraction 54/4 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 54/4 = (54/2) / (4/2) = 27/2

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Given the function
f(x)=2x^(2)+1, find the value of
f(-(5)/(2)) in simplest form.
Answer:

Given the function $f(x)=2 x^{2}+1$ , find the value of $f\left(-\frac{5}{2}\right)$ 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}+1

, find the value of

f\left(-\frac{5}{2}\right)

in simplest form.

\newline

Answer:

Substitute $x$ in function: Substitute the value of $x$ into the function. $\newline$ We are given $f(x) = 2x^2 + 1$ and we need to find $f\left(-\left(\frac{5}{2}\right)\right)$ . So we will substitute $x$ with $-\left(\frac{5}{2}\right)$ in the function. $\newline$ $f\left(-\left(\frac{5}{2}\right)\right) = 2\left(-\left(\frac{5}{2}\right)\right)^2 + 1$
Simplify negative square: Simplify the exponent. $\newline$ We need to square $-\left(\frac{5}{2}\right)$ . Remember that when you square a negative number, the result is positive. $\newline$ $\left(-\left(\frac{5}{2}\right)\right)^2 = \left(-\frac{5}{2}\right) \times \left(-\frac{5}{2}\right) = \frac{25}{4}$
Multiply by $2$ : Multiply the result by $2$ . Now we multiply the squared value by $2$ as per the function. $2 \times \left(\frac{25}{4}\right) = \frac{50}{4}$
Simplify function: Simplify the function. $\newline$ We now have all the parts to simplify the function. $\newline$ $f(-\frac{5}{2}) = \frac{50}{4} + 1$
Convert constant to common denominator: Convert the constant term to have a common denominator with the fraction. $\newline$ To add the fraction and the constant term, we need a common denominator. The number $1$ can be written as $\frac{4}{4}$ . $\newline$ $1 = \frac{4}{4}$
Add fraction and constant: Add the fraction and the constant term. $\newline$ Now we add the two terms together. $\newline$ $\frac{50}{4} + \frac{4}{4} = \frac{54}{4}$
Simplify final fraction: Simplify the fraction. $\newline$ The fraction $\frac{54}{4}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{54}{4} = \left(\frac{54}{2}\right) / \left(\frac{4}{2}\right) = \frac{27}{2}$