Question

Consider f(x)=root(x-5)

Find the value of x for which f is undefined


Explain in detail please! I’m pretty stupid so...

Answer 1

x < 5

Explanation:

f(x) = √(x−5)

f(x) is undefined when the expression under the radical is negative.

x − 5 < 0

x < 5

Therefore, f(x) is undefined when x is less than 5.

Answer 2

The function f(x) =
`\sqrt{(x - 5)` is undefined for all real numbers x that are less than 5. This includes all negative numbers, zero, and any fraction or irrational number whose value is less than 5.

The function f(x) =
`\sqrt{(x - 5)`defines the square root of the difference between the input value x and the constant 5. Since a square root always returns a non-negative number, the expression under the radical, x - 5, must be non-negative for the function to be defined at any input value x. This means that the radicand, x - 5, cannot be less than zero.

To determine the values of x where the function is undefined, we set the radicand equal to zero and solve the resulting inequality:

x - 5 = 0

Solving for x, we get:

x = 5

Therefore, the function f(x) =
`\sqrt{(x - 5)` is undefined for all real numbers x that are less than 5. This includes all negative numbers, zero, and any fraction or irrational number whose value is less than 5.

Complete question below:

Consider the function f(x) =
`\sqrt{(x - 5)`. For which values of x is f(x) undefined?