Question

f(x) = x + 7 and g(x) = x - 2, I honestly have no clue where to start im confused

Answer 1

Answer: A) {x | x ≠ 2}

Step-by-step explanation:

Domain is: all the values that x can be. Look for the following restrictions:

• denominator (bottom) cannot be zero (set denomiantor ≠ zero)
• square root cannot be negative (set inside of square root ≥ 0)
• logs must be positive (set log > 0)

$\frac{f(x)}{g(x)} = \frac{x+7}{x-2}$

denominator is: x - 2 so set it unequal to zero and solve.

x - 2 ≠ 0

  +2   +2

x     ≠  2

Answer 2

Steps:

So for this question, it asks us for the domain of f(x) ÷ g(x). Set up our function as such:

$(\frac{f}{g})(x)=\frac{x+7}{x-2}$

Next, we want to find the discontinuity of this function, or the value(s) in which the function cannot equal to. In this case, we need to find the x value that makes the denominator equal to 0 (as anything divided by 0 is undefined). To find it, set the denominator to 0 and solve as such:

$x-2\neq 0\\x\neq 2$

Answer:

With the information that we have, the answer is $\{x\ |\ x\neq 2\}$, or the first option.