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

Understand function transformation: Understand the function transformation. We are given the function f(x) = -x^2 + 1/2 and we need to find f(x-1). This means we will substitute (x-1) for x in the function f(x).Substitute into function: Substitute (x-1) into the function. f(x-1) = -(x-1)^2 + 1/2Expand square term: Expand the square term. f(x-1) = -[(x-1)(x-1)] + 1/2 f(x-1) = -[x^2 - 2x + 1] + 1/2Distribute and simplify: Distribute the negative sign and simplify. f(x-1) = -x^2 + 2x - 1 + 1/2 f(x-1) = -x^2 + 2x - 1/2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

Home

Math Problems

Algebra 2

Composition of linear and quadratic functions: find an equation

Full solution

Q. Given the function

f(x)=-x^{2}+\frac{1}{2}

, then what is

f(x-1)

as a simplified polynomial?

\newline

Answer:

Understand function transformation: Understand the function transformation. $\newline$ We are given the function $f(x) = -x^2 + \frac{1}{2}$ and we need to find $f(x-1)$ . This means we will substitute $(x-1)$ for $x$ in the function $f(x)$ .
Substitute into function: Substitute $(x-1)$ into the function. $f(x-1) = -(x-1)^2 + \frac{1}{2}$
Expand square term: Expand the square term. $\newline$ $f(x-1) = -[(x-1)(x-1)] + \frac{1}{2}$ $\newline$ $f(x-1) = -[x^2 - 2x + 1] + \frac{1}{2}$
Distribute and simplify: Distribute the negative sign and simplify. $\newline$ $f(x-1) = -x^2 + 2x - 1 + \frac{1}{2}$ $\newline$ $f(x-1) = -x^2 + 2x - \frac{1}{2}$