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

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:

[tex] \frac{7-3x}{4x-9} [/tex]

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

[tex] \frac{7-3(\frac{9}{4})}{4(\frac{9}{4})-9} = \frac{whatever}{0} [/tex]

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.

AnimeBrainly AnimeBrainly · Answer 2 · 2018-07-27T19:52:28+02:00

(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