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san4es73 [151]
3 years ago
6

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

Mathematics
2 answers:
Phoenix [80]3 years ago
4 0
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.
suter [353]3 years ago
3 0

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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