Given the function f(x)=(6)/(5)+(3)/(2)x^(2), then what is f(x-2) as a simplified polynomial? Answer:

Understand Function: Understand the function and what is being asked. We are given the function f(x) = (6/5) + (3/2)x^2 and we need to find f(x-2). This means we need to substitute (x-2) for x in the function f(x).Substitute x-2: Substitute (x-2) for x in the function f(x). f(x-2) = (6/5) + (3/2)(x-2)^2Expand Squared Term: Expand the squared term (x-2)^2. (x-2)^2 = x^2 - 4x + 4Substitute Expanded Term: Substitute the expanded term back into the function. f(x-2) = (6/5) + (3/2)(x^2 - 4x + 4)Distribute Constant: Distribute the (3/2) across the terms in the parentheses. f(x-2) = (6/5) + (3/2)x^2 - (3/2)*4x + (3/2)*4Simplify Expression: Simplify the expression by multiplying the constants. f(x-2) = (6/5) + (3/2)x^2 - 6x + 6Combine Constant Terms: Combine the constant terms (6/5) and 6. f(x-2) = (6/5) + 6 + (3/2)x^2 - 6x To combine (6/5) and 6, we need to express 6 as a fraction with a denominator of 5. 6 = (30/5) f(x-2) = (6/5) + (30/5) + (3/2)x^2 - 6xAdd Constant Fractions: Add the constant fractions. f(x-2) = (36/5) + (3/2)x^2 - 6xWrite Final Polynomial: Write the final simplified polynomial. f(x-2) = (3/2)x^2 - 6x + (36/5)

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Given the function
f(x)=(6)/(5)+(3)/(2)x^(2), then what is
f(x-2) as a simplified polynomial?
Answer:

Given the function $f(x)=\frac{6}{5}+\frac{3}{2} x^{2}$ , then what is $f(x-2)$ as a simplified polynomial? $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find an equation

Full solution

Q. Given the function

f(x)=\frac{6}{5}+\frac{3}{2} x^{2}

, then what is

f(x-2)

as a simplified polynomial?

\newline

Answer:

Understand Function: Understand the function and what is being asked. $\newline$ We are given the function $f(x) = \frac{6}{5} + \frac{3}{2}x^2$ and we need to find $f(x-2)$ . This means we need to substitute $(x-2)$ for $x$ in the function $f(x)$ .
Substitute $x-2$ : Substitute $(x-2)$ for $x$ in the function $f(x)$ . $\newline$ $f(x-2) = \frac{6}{5} + \frac{3}{2}(x-2)^2$
Expand Squared Term: Expand the squared term $(x-2)^2$ . $(x-2)^2 = x^2 - 4x + 4$
Substitute Expanded Term: Substitute the expanded term back into the function. $\newline$ $f(x-2) = \frac{6}{5} + \frac{3}{2}(x^2 - 4x + 4)$
Distribute Constant: Distribute the $(\frac{3}{2})$ across the terms in the parentheses. $f(x-2) = \left(\frac{6}{5}\right) + \left(\frac{3}{2}\right)x^2 - \left(\frac{3}{2}\right)\cdot 4x + \left(\frac{3}{2}\right)\cdot 4$
Simplify Expression: Simplify the expression by multiplying the constants. $f(x-2) = \frac{6}{5} + \frac{3}{2}x^2 - 6x + 6$
Combine Constant Terms: Combine the constant terms $(\frac{6}{5})$ and $6$ .
$f(x-2) = (\frac{6}{5}) + 6 + (\frac{3}{2})x^2 - 6x$
To combine $(\frac{6}{5})$ and $6$ , we need to express $6$ as a fraction with a denominator of $5$ .
$6 = (\frac{30}{5})$
$f(x-2) = (\frac{6}{5}) + (\frac{30}{5}) + (\frac{3}{2})x^2 - 6x$
Add Constant Fractions: Add the constant fractions. $f(x-2) = \frac{36}{5} + \frac{3}{2}x^2 - 6x$
Write Final Polynomial: Write the final simplified polynomial. $\newline$ $f(x-2) = \frac{3}{2}x^2 - 6x + \frac{36}{5}$