Advertisements
Advertisements
Question
Find the range of the following functions given by f(x) = |x − 3|
Solution
We know |x| are defined for all real values.
And |x – 3| will always be greater than or equal to 0.
i.e., f(x) ≥ 0
Therefore, the range of f = `[0, oo)`
APPEARS IN
RELATED QUESTIONS
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(b) pre-images of 6, −3 and 5.
f, g, h are three function defined from R to R as follow:
(ii) g(x) = sin x
Find the range of function.
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(i) f + g
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
Write the domain and range of function f(x) given by
Let f(x) = x, \[g\left( x \right) = \frac{1}{x}\] and h(x) = f(x) g(x). Then, h(x) = 1
If f(m) = m2 − 3m + 1, find f(− x)
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 3), (4, 1), (2, 2)}
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
Find the domain and range of the following function.
f(x) = 7x2 + 4x − 1
An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain
Express the following logarithmic equation in exponential form
log10 (0.001) = −3
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Find the domain of f(x) = log10 (x2 − 5x + 6)
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Given the function f: x → x2 – 5x + 6, evaluate f(2)
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
A graph representing the function f(x) is given in it is clear that f(9) = 2
What is the image of 6 under f?
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.