Question

What are the domain and range of the function f(x)= -log(5-x)+9?

O domain: x <5

range: y29

O domain: x 5

range: (-00,00)

domain: 29

range: (-00,00)

domain: 29

range: y29

Answer 1

The domain of a function are the values that x can take and the range are the values that take y.

Then,

since the function g(x)=log(x) isn't defined for
`x\leq0`, then

log(5-x) doesn't exist when
`5-x\leq0,\;  5\leq x`

So, the x can not take the values of x sucht that 5\leq x. Therefore, the domain of f(x) are
`x<5`

Now, observe that the range of f(x) is the set of the real numbers from 5. since 5 is a horizontal asymptote of f.