Let g(x)=(x^(2)-x-12)/(x-4) when x!=4. g is continuous for all real numbers. Find g(4). Choose 1 answer: (A) 4 (B) -3 (C) -4 (D) 7

Simplify function g(x): First, we need to simplify the function g(x) to find a form that can be evaluated at x = 4, since the original form has a discontinuity at x = 4. We will factor the numerator of g(x). Calculation: Factor x^2 - x - 12. x^2 - x - 12 = (x - 4)(x + 3)Cancel out common factor: Now that we have factored the numerator, we can simplify the function by canceling out the common factor in the numerator and the denominator. Calculation: Simplify (x - 4)(x + 3) / (x - 4). g(x) = (x + 3) when x ≠ 4Evaluate g(4): Since g is continuous for all real numbers, the value of g(4) must be the same as the limit of g(x) as x approaches 4. We can now substitute x = 4 into the simplified form of g(x). Calculation: Evaluate g(4). g(4) = 4 + 3 = 7

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Algebra 2

Conjugate root theorems

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Q. Let

g(x)=\frac{x^{2}-x-12}{x-4}

when

x \neq 4

\newline

g

is continuous for all real numbers.

\newline

Find

g(4)

\newline

Choose

1

answer:

\newline

(A)

4

\newline

(B)

-3

\newline

(C)

-4

\newline

(D)

7

Simplify function $g(x)$ : First, we need to simplify the function $g(x)$ to find a form that can be evaluated at $x = 4$ , since the original form has a discontinuity at $x = 4$ . We will factor the numerator of $g(x)$ . $\newline$ Calculation: Factor $x^2 - x - 12$ . $\newline$ $x^2 - x - 12 = (x - 4)(x + 3)$
Cancel out common factor: Now that we have factored the numerator, we can simplify the function by canceling out the common factor in the numerator and the denominator. $\newline$ Calculation: Simplify $(x - 4)(x + 3) / (x - 4)$ . $\newline$ g(x) = $(x + 3)$ when $x \neq 4$
Evaluate $g(4)$ : Since $g$ is continuous for all real numbers, the value of $g(4)$ must be the same as the limit of $g(x)$ as $x$ approaches $4$ . We can now substitute $x = 4$ into the simplified form of $g(x)$ . $\newline$ Calculation: Evaluate $g(4)$ . $\newline$ $g(4) = 4 + 3 = 7$