Answered

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Consider functions [tex]f[/tex] and [tex]g[/tex]:

[tex]\[
\begin{array}{l}
f(x) = x^2 + 7x \\
g(x) = 3x - 1
\end{array}
\][/tex]

What is the value of [tex](f \circ g)(x)[/tex]?

A. [tex]3x^2 + 21x + 1[/tex]
B. [tex]3x^2 + 7x - 1[/tex]
C. [tex]9x^2 + 21x - 1[/tex]
D. [tex]9x^2 + 15x - 6[/tex]

Sagot :

GinnyAnswer
To find [tex]\((f \circ g)(x)\)[/tex], we need to substitute [tex]\(g(x)\)[/tex] into [tex]\(f(x)\)[/tex]. Let's first identify the functions:

[tex]\[ f(x) = x^2 + 7x \][/tex]
[tex]\[ g(x) = 3x - 1 \][/tex]

We want to find [tex]\(f(g(x))\)[/tex]. This means substituting [tex]\(3x - 1\)[/tex] into [tex]\(f(x)\)[/tex]:

[tex]\[ f(g(x)) = f(3x - 1) \][/tex]

Now, plug [tex]\(3x - 1\)[/tex] in place of [tex]\(x\)[/tex] in [tex]\(f(x)\)[/tex]:

[tex]\[ f(3x - 1) = (3x - 1)^2 + 7(3x - 1) \][/tex]

First, let's expand [tex]\((3x - 1)^2\)[/tex]:

[tex]\[ (3x - 1)^2 = 9x^2 - 6x + 1 \][/tex]

Next, let's distribute the 7 in [tex]\(7(3x - 1)\)[/tex]:

[tex]\[ 7(3x - 1) = 21x - 7 \][/tex]

Now, add these two expressions together:

[tex]\[ (9x^2 - 6x + 1) + (21x - 7) \][/tex]

Combine like terms:

[tex]\[ 9x^2 - 6x + 1 + 21x - 7 = 9x^2 + 15x - 6 \][/tex]

Therefore, the value of [tex]\((f \circ g)(x)\)[/tex] is:

[tex]\[ 9x^2 + 15x - 6 \][/tex]

So, the correct answer is:

D. [tex]\(9 x^2+15 x-6\)[/tex]
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