Question

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

Answer 1

Answer:

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 $x$

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.