Math Questions With Answers (7): Domain of Function

Questions on finding domain of functions, including logarithmic , exponential, rational, square root and many other functions are presented along with their answers located in the lower part of the page.

Question 1

Find the domain of f(x) = 2x + 7.

Question 2

What is the domain of g(x) = 1 / (- x + 8).

Question 3

Find the domain of h(x) = (x - 6) / (2x - 8).

Question 4

What is the domain of f(x) = 5 / √(-x + 4)?

Question 5

Find the domain of h(x) = √(-x + 5) / √(x - 3).

Question 6

Find the domain of f(x) = √(|x| - 5).

Question 7

Find the domain of f(x) = √(|3x - 8| - 5).

Question 8

Find the domain of f(x) = (3x - 6) / (x² + 2x - 8).

Question 9

Find the domain of h(x) = (3x - 6) / √ (x² + 2x - 8).

Question 10

Find the domain of g(x) = |2x - 4|.

Question 11

Find the domain of h(x) = ln(|2x - 9|).

Question 12

Find the domain of g(x) = 1 / (x² + 6).

Question 13

Find the domain of g(x) = 1 / √( x² + 2x + 6).

Question 14

Find the domain of h(x) = 1 / √( | - x² - 9 | ).

Question 15

What is the domain of function g defined by a set of ordered pairs as follows: g = {( 3 , 2 ) , ( 5 , 9) , ( 6 , 9 ) , (11 , 0 )}?

Question 16

Find the domain of g(x) = 1 / [ 2 - √( x + 2 ) ].

Question 17

What is the domain of f(x) = e^ln(x)

Question 18

What is the domain of f(x) = 1 / Log(2x - 3)?

Question 19

Find the domain of g(x) = ln (2x - 8)

Question 20

Find the domain of g(x) = Log (x² + 3x - 10).

ANSWERS TO ABOVE QUESTIONS

1) (- ∞ , + ∞)
2) (- ∞ , 8) U (8 , + ∞)
3) (- ∞ , 4) U (4 + ∞)
4) (- ∞ , 4)
5) (3 , 5]
6) (- ∞ , -5] U [5 , + ∞)
7) (- ∞ , 1] U [13/3 , + ∞)
8) (- ∞ , -4) U (-4 , 2) U (2 , + ∞)
9) (- ∞ , -4) U (2 , + ∞)
10) (- ∞ , + ∞)
11) (- ∞ , 9/2) U (9/2 , + ∞)
12) (- ∞ , + ∞)
13) (- ∞ , + ∞)
14) (- ∞ , + ∞)
15) {3 , 5 , 6 , 11}
16) [- 2 , 2) U (2 , + ∞)
17) (0 , + ∞)
18) (3/2 , 2) U (2 , + ∞)
19) (4 , + ∞)
20) (- ∞ , -5) U (2 , + ∞)