Advertisements
Advertisements
Question
Find the range of the following function.
f(x) = x2 + 2, x, is a real number.
Solution
f(x) = x2 + 2, x, is a real number
The values of f(x) for various values of real numbers x can be written in the tabular form as
| x | 0 | ±0.3 | ±0.8 | ±1 | ±2 | ±3 | ... |
| f(x) | 2 | 2.09 | 2.64 | 3 | 6 | 11 | ... |
Thus, it can be clearly observed that the range of f is the set of all real numbers greater than 2.
i.e., range of f = [2,`oo`)
Alter:
Let x be any real number.
Accordingly,
x2 ≥ 0
⇒ x2 + 2 ≥ 0 + 2
⇒ x2 + 2 ≥ 2
⇒ f(x) ≥ 2
∴ Range of f = [2, `oo`)
APPEARS IN
RELATED QUESTIONS
Find the domain and range of the given real function:
f(x) = – |x|
Find the domain and range of the following real function:
f(x) = `sqrt(9 - x^2)`
A function f is defined by f(x) = 2x – 5. Write down the values of f(0).
The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by `t(C) = "9C"/5 + 32`
Find
(i) t(0)
(ii) t(28)
(iii) t(–10)
(iv) The value of C, when t(C) = 212.
Find the range of the following function.
f(x) = 2 – 3x, x ∈ R, x > 0.
Find the range of the following function.
f(x) = x, x is a real number
Find the domain and the range of the real function f defined by `f(x)=sqrt((x-1))`
Find the domain and the range of the real function f defined by f (x) = |x – 1|.
Let `f = {(x, x^2/(1+x^2)):x ∈ R}` be a function from R into R. Determine the range of f.
If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:
(i) A × B
If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:
(ii) B × A
If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:
(iii) A × A
If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:
(iv) B × B
The function f is defined by
If f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = x2 + 1, then find f + g
If [x]2 – 5[x] + 6 = 0, where [ . ] denote the greatest integer function, then ______.
If f(x) = ax + b, where a and b are integers, f(–1) = – 5 and f(3) = 3, then a and b are equal to ______.
