Question

49 points, will give Brainliest! Having a lot of trouble with Determining the domains of functions. Khan Academy Algebra I.

Answer 1

Domains of functions are the values that can be plugged into the function and not "break" it. By "break" I mean that the denominator cannot be 0, in this case. If the denominator is 0, we will get a divide by 0 error, and thus, we must restrict the domain. All values of x will work except 9/4:

$\frac{7-3x}{4x-9}$

Let's plug in 9/4 and see what happens:

$\frac{7-3(\frac{9}{4})}{4(\frac{9}{4})-9} = \frac{whatever}{0}$

So, plugging in 9/4 results in denominator equalling 0. Therefore, we must restrict the domain so that x ≠ 9/4. Your answer is All real values of x such that x ≠ 9/4.

Answer 2

(D) All real values of x such that x ≠ 9/4 should be your answer

Remember that if there is a 0 in the denominator, the answer will be 'undefined'

The only number that does not work in the equation is 9/4 because:

f(x) = (7 - 3(9/4))/(4(9/4) - 9)

Simplify

f(x) = (7 - 27/4)/(9 - 9)

Simplify

f(x) = (7 - 27/4)/(0) = undefined

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Therefore, (D) is your best choice

hope this helps