QuestionThe function $f(x)=x^{2}+1$ and $g(x)=3-x$ , determine an equation for the combined function $y=f(x)-g(x)$ . $y=x^{2}-x+2$ $y=x^{2}+x-2$ $y=x^{2}+x+4$ $y=x^{2}-x+4$

Studdy Solution

STEP 1

1. We are given two functions, $f(x) = x^2 + 1$ and $g(x) = 3 - x$ .
2. We need to find an equation for the combined function $y = f(x) - g(x)$ .
3. We will perform algebraic operations to combine these functions.

STEP 2

1. Substitute the given functions into the equation $y = f(x) - g(x)$ .
2. Simplify the resulting expression.

STEP 3

Substitute the expressions for $f(x)$ and $g(x)$ into the equation for $y$ :
$y = (x^2 + 1) - (3 - x)$

STEP 4

Distribute the negative sign and simplify the expression:
$y = x^2 + 1 - 3 + x$
Combine like terms:
$y = x^2 + x + 1 - 3$
$y = x^2 + x - 2$
The equation for the combined function is:
$\boxed{y = x^2 + x - 2}$

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