Question

range of f(x)=|x-5| / x-5 is

Answer 1

Answer:

f(x) is defined for all real no. except x-5=0

|x-5|

x-5. is signum function=|x|

x

|x|=x if x>0

|x|= -x if x<0

|x|

x. =1.

|x| = -1

-x.

therefore range= {-1,1} (set of 1 and -1)

Answer 2

The range of f(x) = |x-5|/(x-5) is {-1,0,1}.

Given,

A function f(x) = |x-5|/(x-5).

To Find,

The range of the given function.

Solution,

The given function is

f(x) = |x-5|/(x-5)

Let us assume that (x-5) = X

So, the function becomes

f(x) = |X| / X = sgn(X)

where, sgn is signum function.

Now, we know that the range of a signum function is {-1,0,1}

And the domain of the signum function is R.

So, the function f(x) = |x-5|/(x-5), behaves as a signum function and it will have the range and domain same as that of a signum function.

Hence, the range of f(x) = |x-5|/(x-5) is {-1,0,1}.

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