Domain and range of a function:
The set X is known as the domain of the function. 'ƒ' and set Y is known as the co-domain. The group of the image of all components of X under the function 'ƒ' is known as the range of 'ƒ' and is shown by ƒ(x). It is clear that range should be a subset of co-domain as we can have few components in co-domain which are not the images of any element of the set X.
Therefore range of 'ƒ' i.e. ƒ(x) = {ƒ(x): x ∈ X}. Clearly ƒ(x) ⊆ Y
Illustration: Calculate the domain of ![601_function1.png](https://www.expertsmind.com/../CMSImages/601_function1.png)
Key concept: Denominator could be non-zero for any function
Solution: x2 - 4 ≠ 0 => x ≠ ± 2
Therefore domain is R - {-2, 2}
Illustration: Calculate the domain of ![117_function2.png](https://www.expertsmind.com/../CMSImages/117_function2.png)
Key concept: Expression under given even root (i.e. square root, fourth root, sixth root etc) could not be negative.
Solution: f(x) is described when
....(1)
Case 1: x ≥0 ƒ(x) = x/x-1
For domain ![2014_function4.png](https://www.expertsmind.com/../CMSImages/2014_function4.png)
x∈[0,1).......(2)
Case 2: x < 0 ![1870_function5.png](https://www.expertsmind.com/../CMSImages/1870_function5.png)
For domain ![760_function6.png](https://www.expertsmind.com/../CMSImages/760_function6.png)
Rejecting the values of x∈[0,∞) because they don't assure the inequality
x < 0.
We obtain x∈(-∞,-1)......(3)
Taking union of (2) and (3)
Domain =![951_function7.png](https://www.expertsmind.com/CMSImages/951_function7.png)
Email based Domain and range of a function Assignment Help -Domain and range of a function Homework Help
We at www.expertsmind.com offer email based Domain and range of a function assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work