Find the domain and the range of each of the following real function:

1.	Find the domain and the range of each of the following real function: f(x) = \(\frac{\|x-4\|}{x-4}\)
Answer» Given: f(x) = \(\frac{\|x-4\|}{x-4}\) Need to find: Where the functions are defined. To find the domain of the function f(x) we need to equate the denominator of the function to 0. Therefore, x – 4 = 0 ⇒ x = 4 It means that the denominator is zero when x = 4 So, the domain of the function is the set of all the real numbers except 4. The domain of the function, D_f(x) = (- ∞, 4) ∪ (4, ∞). The numerator is an absolute function of the denominator. So, for any value of x from the domain set, we always get either +1 or -1 as the output. So, the range of the function is a set containing -1 and +1 Therefore, the range of the function, R_f(x) = { -1 , 1 }

Find the domain and the range of each of the following real function: f(x) = \(\frac{|x-4|}{x-4}\)

Answer»

Given: f(x) = \(\frac{|x-4|}{x-4}\)

Need to find: Where the functions are defined.

To find the domain of the function f(x) we need to equate the denominator of the function to 0.

Therefore,

x – 4 = 0

⇒ x = 4

It means that the denominator is zero when x = 4

So, the domain of the function is the set of all the real numbers except 4.

The domain of the function, D_f(x) = (- ∞, 4) ∪ (4, ∞).

The numerator is an absolute function of the denominator. So, for any value of x from the domain set, we always get either +1 or -1 as the output. So, the range of the function is a set containing -1 and +1

Therefore, the range of the function, R_f(x) = { -1 , 1 }

Discussion

No Comment Found

Related InterviewSolutions

Find fog and gof, if (i) f(x) = ex, g(x) = loge x(ii) f(x) = x2, g(x) = cos x(iii) f(x) = |x|, g(x) = sin x(iv) f(x) = x + 1, g(x) = ex(v) f(x) = sin−1 x, g(x) = x2
Write the names of any two C++ header files.
List the names of any two functions of iostream.h header file.
Pick the odd one out from the following and give reason.gets() getline() getch() getchar()
What is the main function of iostream.h header file?
In a C++ program, you forgot to include the header file iostream.h. What are the possible errors occur in that Program? Explain ?
Let ` f(x) =sqrt(9-x^(2))." then , dom " (f ) =?`A. `[-3,3]`B. `(-oo,-3]`C. `[3,oo)`D. `(-oo,-3] uu (4,oo)`
Let `f(x)=sqrt(cos x).` Then dom (f ) =?A. `[0.(pi)/(2)]`B. `[(3pi)/(2),2pi]`C. `[0,(pi)/(2)]uu[(3pi)/(2),2pi]`D. none of these
Let `f(x) = log (1-x) +sqrt(x^(2)-1). `Then dom (f )=?A. `(1,oo)`B. `(-oo,-1]`C. `[-1,1]`D. `(0,1)`
Let `A={1,2}andB={2,4,6}."Let "f={x,y):x""inA,yinBandandygt2x+1}`. Write f as a set of ordered paris. Show that f is a relation but not a function from A to B.