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If [tex]\( f(x) = x^2 + 1 \)[/tex] and [tex]\( g(x) = 3x + 1 \)[/tex], find [tex]\( [f(2) - g(1)]^2 \)[/tex].

A. 1
B. 2
C. 9

Sagot :

GinnyAnswer
Of course, let's solve this step-by-step:

Given the functions:
[tex]\[ f(x) = x^2 + 1 \][/tex]
[tex]\[ g(x) = 3x + 1 \][/tex]

First, we need to find [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 2^2 + 1 \][/tex]
[tex]\[ f(2) = 4 + 1 \][/tex]
[tex]\[ f(2) = 5 \][/tex]

Next, we find [tex]\( g(1) \)[/tex]:
[tex]\[ g(1) = 3 \cdot 1 + 1 \][/tex]
[tex]\[ g(1) = 3 + 1 \][/tex]
[tex]\[ g(1) = 4 \][/tex]

Now, we need to compute [tex]\( f(2) - g(1) \)[/tex]:
[tex]\[ f(2) - g(1) = 5 - 4 \][/tex]
[tex]\[ f(2) - g(1) = 1 \][/tex]

Finally, we square this result to find [tex]\([f(2) - g(1)]^2\)[/tex]:
[tex]\[ [f(2) - g(1)]^2 = 1^2 \][/tex]
[tex]\[ [f(2) - g(1)]^2 = 1 \][/tex]

Therefore, the answer is:
[tex]\[ 1 \][/tex]
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