Question

Blanks
If f(x)=x²-x²+2 then f (-2)
2x If x² -1 is divided by X-1 then remaindes is
3. If a
polynomial x - xt2 is divided by
x+/ then remainder is
4. Degre are the tc is
if
a; B; c ER​

Answer 1

Explanation:

The most difficult part of combining functions is understanding the notation. What does (f\cdot g)(x)(f⋅g)(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis mean?

Well, (f\cdot g)(x)(f⋅g)(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis just means to find the product of f(x)f(x)f, left parenthesis, x, right parenthesis and g(x)g(x)g, left parenthesis, x, right parenthesis. Mathematically, this means that (f\cdot g)(x)=f(x)\cdot g(x)(f⋅g)(x)=f(x)⋅g(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis, equals, f, left parenthesis, x, right parenthesis, dot, g, left parenthesis, x, right parenthesis.

Now, this becomes a familiar problem.

\begin{aligned} (f\cdot g)(x) &= f(x)\cdot g(x)&\gray{\text{Define.}} \\\\ &= \left(2x-3\right)\cdot\left(x+1\right) &\gray{\text{Substitute.}} \\\\ &= 2x^2+2x-3x-3&\gray{\text{Distribute.}} \\\\ &=2x^2-x-3&\gray{\text{Combine like terms.}} \end{aligned}

(f⋅g)(x)

=f(x)⋅g(x)

=(2x−3)⋅(x+1)

=2x

2

+2x−3x−3

=2x

2

−x−3

Define.

Substitute.

Distribute.

Combine like terms.