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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.

Respuesta :

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ANSWER

Yes,
[tex]x > 5[/tex]
is the restriction.

EXPLANATION

The given function is

[tex]f(x) = log(x - 5) + 1[/tex]

This is a logarithmic function that is defined for

[tex]x - 5 > 0[/tex]

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,

[tex]x > 5[/tex]

Therefore the the restrictions is that,

[tex]x > 5[/tex]

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

Answer:

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

2) Restriction for domain; x>5

Step-by-step 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.




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