g(x)= 8/10-9x
would the correct answer be
a) {xIx is a real number and x ==/== 10/9?
b){xIxis a real number and x equals lesser or equal to >_ 10/9
c){xIx is a real number and x =/= 0
d){xIx is a real number and x =/= 8
my answer is c is this correct?
No, c is not correct.
In each of the other cases, what happens when x is the number given:
a) 8/(10-90/9)
b) x < 10/9, say 1/9 -> 8/(10-9/9)
d) 8/(10-72)
One of these three is undefined. Which?
would the answer be d?
On what grounds do you choose d?
To determine the correct answer, let's analyze the given function g(x) = 8/(10 - 9x).
The denominator of the function is 10 - 9x. A fraction is undefined when the denominator equals zero since division by zero is not allowed. Therefore, to determine the restrictions on x, we need to find when the denominator is equal to zero.
Setting the denominator equal to zero and solving for x:
10 - 9x = 0
9x = 10
x = 10/9
Now, we have found that x = 10/9 is the value of x that makes the function undefined.
Now let's evaluate the answer options:
a) {x| x is a real number and x != 10/9}: This answer option states that x can be any real number except for x = 10/9, which is the correct restriction we found. So, option a) seems plausible.
b) {x| x is a real number and x ≤ 10/9}: This option restricts x to be less than or equal to 10/9. However, the correct restriction is that x cannot be equal to 10/9, so this option is not correct.
c) {x| x is a real number and x != 0}: This option states that x can be any real number except for x = 0, and this restriction is not valid for the given function. So, option c) is not correct.
d) {x| x is a real number and x != 8}: This option restricts x to be any real number except for x = 8. However, the correct restriction we found earlier is x = 10/9, not x = 8. So, option d) is not correct.
Therefore, the correct answer is a) {x| x is a real number and x != 10/9}.