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Let
f(x)=x-2 and
g(x)=x^(2)+x-1. Find each of the following and simplify.
a)
(fg)(x)=
b)
(fg)(-1)=
c)
(fg)(2)=

Let $f(x)=x-2$ and $g(x)=x^{2}+x-1$ . Find each of the following and simplify. $\newline$ a) $(fg)(x)=$ $\newline$ b) $(fg)(-1)=$ $\newline$ c) $(fg)(2)=$

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Evaluate an exponential function

Full solution

Q. Let

f(x)=x-2

and

g(x)=x^{2}+x-1

. Find each of the following and simplify.

\newline

a)

(fg)(x)=

\newline

b)

(fg)(-1)=

\newline

c)

(fg)(2)=

Find Product of Functions: Let's find the product of the functions $f(x)$ and $g(x)$ , which is denoted as $(fg)(x)$ .
$f(x) = x - 2$
$g(x) = x^2 + x - 1$
To find $(fg)(x)$ , we multiply $f(x)$ by $g(x)$ :
$(fg)(x) = f(x) \cdot g(x)$
$(fg)(x) = (x - 2) \cdot (x^2 + x - 1)$
Now, we distribute $g(x)$ $0$ across the terms in the parentheses:
$g(x)$ $1$
$g(x)$ $2$
Combine like terms:
$g(x)$ $3$
Calculate $(fg)(-1)$ : Now let's evaluate $(fg)(-1)$ . Substitute $-1$ for $x$ in $(fg)(x) = x^3 - x^2 - 3x + 2$ . $(fg)(-1) = (-1)^3 - (-1)^2 - 3(-1) + 2$ $(fg)(-1) = -1 - 1 + 3 + 2$ $(fg)(-1) = 3$
Evaluate $(fg)(2)$ : Finally, let's evaluate $(fg)(2)$ . Substitute $2$ for $x$ in $(fg)(x) = x^3 - x^2 - 3x + 2$ . $(fg)(2) = (2)^3 - (2)^2 - 3(2) + 2$ $(fg)(2) = 8 - 4 - 6 + 2$ $(fg)(2) = 0$

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