Question

What is the domain of the function y = ln (-x+3/2)

a. x<2
b. X>2
c. x<3
d. x>3

Answer 1

Answer:c

Explanation:

Answer 2

Option C is correct.

x < 3

Explanation:

The domain of a function is the set of input or arguments values fpr which the function is real and defined.

For a positive value of logarithmic (ln)

`ln x` , x > 0.

Given:
`y = \ln((-x+3)/(2))`

⇒
`(-x+3)/(2) > 0`

Multiply both sides by 2 we get;

`-x +3 > 0`

or

`-(x-3)>0`

or

x -3 < 0 [ ∵a > b ⇔ -a < -b ]

Add 3 both sides we get;

x -3 +3 < 0 +3

Simplify:

x < 3

therefore, the domain for the given function is, x < 3