Find the domain of the function f(x)=
write your answer in interval notation.

The domain of f is (-∞,4)

Step-by-step explanation:

Domain of a Function

The domain of a function f is the set of all the values that the input variable can take so the function exists.

We are given the function

It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:

4 - x > 0

Subtracting 4:

- x > -4

Multiplying by -1 and swapping the inequality sign:

x < 4

Thus the domain of f is (-∞,4)

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5