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If [tex][tex]$f(x)=x^3-2x^2+3x-5$[/tex][/tex] and [tex][tex]$g(x)=x^2+x-1$[/tex][/tex], perform the given function operation.

Find [tex][tex]$f(x)-g(x)$[/tex][/tex].

Sagot :

GinnyAnswer
Certainly! Let's go through the process of finding [tex]\( f(x) - g(x) \)[/tex] step-by-step.

First, let's review the given functions:

[tex]\[ f(x) = x^3 - 2x^2 + 3x - 5 \][/tex]
[tex]\[ g(x) = x^2 + x - 1 \][/tex]

Our goal is to find [tex]\( f(x) - g(x) \)[/tex]. To achieve this, we subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex]:

[tex]\[ f(x) - g(x) = (x^3 - 2x^2 + 3x - 5) - (x^2 + x - 1) \][/tex]

Next, we distribute the negative sign through the second polynomial:

[tex]\[ f(x) - g(x) = x^3 - 2x^2 + 3x - 5 - x^2 - x + 1 \][/tex]

Now, we combine like terms:

1. The [tex]\( x^3 \)[/tex] term:
[tex]\[ x^3 \][/tex]

2. The [tex]\( x^2 \)[/tex] terms:
[tex]\[ -2x^2 - x^2 = -3x^2 \][/tex]

3. The [tex]\( x \)[/tex] terms:
[tex]\[ 3x - x = 2x \][/tex]

4. The constant terms:
[tex]\[ -5 + 1 = -4 \][/tex]

Putting it all together, we get:

[tex]\[ f(x) - g(x) = x^3 - 3x^2 + 2x - 4 \][/tex]

Therefore, the result of the function operation [tex]\( f(x) - g(x) \)[/tex] is:

[tex]\[ f(x) - g(x) = x^3 - 3x^2 + 2x - 4 \][/tex]
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