Question

For each of the following functions, identify any restrictions on its domain.

F(x) = log(x-5)+1

-Is there any value of x that would cause this function to be undefined?
-If there are restrictions on the domain, explain those restrictions.
-If there are no restrictions, explain why that is.

Answer 1

ANSWER

Yes,

`x > 5`
is the restriction.

EXPLANATION

The given function is


`f(x) = log(x - 5) + 1`

This is a logarithmic function that is defined for


`x - 5 > 0`

The reason is that, the logarithmic functions are not defined for negative values of x and 0.

Therefore the argument must always be positive.

When we solve the above inequality, we get,


`x > 5`

Therefore the the restrictions is that,


`x > 5`

This is also the same as the domain of the function.

Answer 2

1) F(x) is not defined for x=5

2) Restriction for domain; x>5

Explanation:

Here the given function is F(x) = log(x-5) +1

In this function if we put the value x =5 then F(5) becomes

F(5) = log(5-5) +1

F(5) = log 0 +1 = ∞

Which indicates that the function F(x) is not defined at x=5.

Now we know that for any negative value of x, logx is not defined Therefore F(x) is defined only for the value of (x-5)>0

Or there is a restriction on domain that x>5.

So there is one restriction on its domain for the given function.