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 g(x): First, we need to simplify the function g(x) to see if we can define it at x = 4, since the original function has a discontinuity at x = 4. g(x) = (x^2 - x - 12) / (x - 4) Factor the numerator to find common factors with the denominator. x^2 - x - 12 can be factored into (x - 4)(x + 3). So, g(x) = [(x - 4)(x + 3)] / (x - 4)Cancel common factor: Next, we cancel out the common factor (x - 4) from the numerator and the denominator, as long as x ≠ 4. g(x) = (x + 3) for x ≠ 4 Now, we can define g(4) by substituting x with 4. g(4) = 4 + 3Define g(4): Calculate the value of g(4). g(4) = 4 + 3 = 7

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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

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) $7$

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Math Problems

Algebra 1

Domain and range of quadratic functions: equations

Full solution

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 $g(x)$ : First, we need to simplify the function $g(x)$ to see if we can define it at $x = 4$ , since the original function has a discontinuity at $x = 4$ .
$g(x) = \frac{x^2 - x - 12}{x - 4}$
Factor the numerator to find common factors with the denominator.
$x^2 - x - 12$ can be factored into $(x - 4)(x + 3)$ .
So, $g(x) = \frac{(x - 4)(x + 3)}{x - 4}$
Cancel common factor: Next, we cancel out the common factor $(x - 4)$ from the numerator and the denominator, as long as $x \neq 4$ .
$g(x) = (x + 3)$ for $x \neq 4$
Now, we can define $g(4)$ by substituting $x$ with $4$ .
$g(4) = 4 + 3$
Define $g(4)$ : Calculate the value of $g(4)$ . $g(4) = 4 + 3 = 7$