Given the function f(x)=(5)/(2)x-(1)/(6), then what is f(x-1) as a simplified polynomial? Answer:

Substitute x-1: Substitute (x-1) into the function f(x). We have the function f(x) = (5/2)x - (1/6). To find f(x-1), we replace every instance of x in the function with (x-1). f(x-1) = (5/2)(x-1) - (1/6)Distribute (5/2): Distribute the (5/2) across the terms inside the parentheses. We need to multiply (5/2) by both x and -1. f(x-1) = (5/2)x - (5/2)(1) - (1/6)Simplify expression: Simplify the expression by performing the multiplication. Now we calculate (5/2)(1) which is 5/2. f(x-1) = (5/2)x - 5/2 - (1/6)Find common denominator: Find a common denominator to combine the constant terms. The common denominator for 2 and 6 is 6. We need to convert -5/2 to a fraction with a denominator of 6. f(x-1) = (5/2)x - (5/2)(3/3) - (1/6)Continue simplifying: Continue simplifying the constant terms. Now we multiply -5/2 by 3/3 to get -15/6. f(x-1) = (5/2)x - 15/6 - (1/6)Combine constant terms: Combine the constant terms. We subtract 1/6 from -15/6 to get -16/6. f(x-1) = (5/2)x - 16/6Simplify constant term: Simplify the constant term if possible. The fraction -16/6 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. f(x-1) = (5/2)x - (16/2)/3 f(x-1) = (5/2)x - 8/3

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Given the function
f(x)=(5)/(2)x-(1)/(6), then what is
f(x-1) as a simplified polynomial?
Answer:

Given the function $f(x)=\frac{5}{2} x-\frac{1}{6}$ , then what is $f(x-1)$ as a simplified polynomial? $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

Full solution

Q. Given the function

f(x)=\frac{5}{2} x-\frac{1}{6}

, then what is

f(x-1)

as a simplified polynomial?

\newline

Answer:

Substitute $x-1$ : Substitute $(x-1)$ into the function $f(x)$ . We have the function $f(x) = \frac{5}{2}x - \frac{1}{6}$ . To find $f(x-1)$ , we replace every instance of $x$ in the function with $(x-1)$ . $f(x-1) = \frac{5}{2}(x-1) - \frac{1}{6}$
Distribute $(5/2)$ : Distribute the $(5/2)$ across the terms inside the parentheses. $\newline$ We need to multiply $(5/2)$ by both $x$ and $-1$ . $\newline$ $f(x-1) = (5/2)x - (5/2)(1) - (1/6)$
Simplify expression: Simplify the expression by performing the multiplication. $\newline$ Now we calculate $(\frac{5}{2})(1)$ which is $\frac{5}{2}$ . $\newline$ $f(x-1) = \left(\frac{5}{2}\right)x - \frac{5}{2} - \left(\frac{1}{6}\right)$
Find common denominator: Find a common denominator to combine the constant terms. $\newline$ The common denominator for $2$ and $6$ is $6$ . We need to convert $-\frac{5}{2}$ to a fraction with a denominator of $6$ . $\newline$ $f(x-1) = \frac{5}{2}x - \left(\frac{5}{2}\right)\left(\frac{3}{3}\right) - \frac{1}{6}$
Continue simplifying: Continue simplifying the constant terms. $\newline$ Now we multiply $-\frac{5}{2}$ by $\frac{3}{3}$ to get $-\frac{15}{6}$ . $\newline$ $f(x-1) = \frac{5}{2}x - \frac{15}{6} - \frac{1}{6}$
Combine constant terms: Combine the constant terms. $\newline$ We subtract $\frac{1}{6}$ from $-\frac{15}{6}$ to get $-\frac{16}{6}$ . $\newline$ $f(x-1) = \frac{5}{2}x - \frac{16}{6}$
Simplify constant term: Simplify the constant term if possible. $\newline$ The fraction $-\frac{16}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $f(x-1) = \frac{5}{2}x - \frac{16}{2}/3$ $\newline$ $f(x-1) = \frac{5}{2}x - \frac{8}{3}$