Q. 305.0( 2 Votes )

# The domain of the function f defined by is equal to

A. (– ∞, – 1) ∪ (1, 4]

B. (– ∞, – 1] ∪ (1, 4]

C. (– ∞, – 1) ∪ [1, 4]

D. (– ∞, – 1) ∪ [1, 4)

Answer :

Given:

To find: the domain of the given function

Explanation: So the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

We have

Now for real value

4-x≥0 and x^{2}-1>0

⇒ 4≥x and x^{2}>1

⇒ x≤4 and -1>x>1

⇒ x≤4 and x>1 and x<-1

⇒ x∈ (-∞, -1)∪(1, 4]

Hence the domain of given function is (-∞, -1)∪(1, 4]

So, the correct answer is option (A)

Rate this question :

Find the domain and range of each of the following real valued functions:

RD Sharma - Mathematics

Write the domain and the range of the function, f(x) = –|x|.

RS Aggarwal - MathematicsFind the domain and the range of the square root function,

f: R^{+} U {0} → R f(x) = for all non-negative real numbers.

Also, draw its graph.

RS Aggarwal - Mathematics

Find the domain of each of the following functions given by

Mathematics - Exemplar

The domain of the function f given by

Mathematics - ExemplarDomain of is

Mathematics - ExemplarFill in the blanks:

Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}

g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}

be two real functions. Then Match the following :

Mathematics - Exemplar

The domain for which the functions defined by f (x) = 3x^{2} – 1 and g (x) = 3 + x are equal is

Find the domain of the function, f(x) = log |x|.

RS Aggarwal - Mathematics