Advertisements
Advertisements
Question
The range of the function f(x) = |x − 1| is
Options
(a) (−∞, 0)
(b) [0, ∞)
(c) (0, ∞)
(d) R
Solution
(b) [0, ∞)
\[\text{ Thus, range} = [0, \infty 0\]
APPEARS IN
RELATED QUESTIONS
Find the domain of the function f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(a) range of f, i.e. f(A).
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.
If f(x) = (a − xn)1/n, a > 0 and n ∈ N, then prove that f(f(x)) = x for all 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:
(v) \[\frac{g}{f}\]
Write the range of the real function f(x) = |x|.
Let f(x) = |x − 1|. Then,
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find `f(1/2)`
Check if the following relation is a function.
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
If f(m) = m2 − 3m + 1, find f(0)
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x3
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Find the domain of f(x) = log10 (x2 − 5x + 6)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Select the correct answer from given alternatives.
If f : R → R is defined by f(x) = x3 then f–1 (8) is equal to :
Select the correct answer from given alternative.
The domain and range of f(x) = 2 − |x − 5| is
Answer the following:
A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
Find the domain of the following function.
f(x) = x!
Answer the following:
Find the range of the following function.
f(x) = |x – 5|
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(x))`
Given the function f: x → x2 – 5x + 6, evaluate f(2)
Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x3 then, find the range of f
If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
Find the domain of the following functions given by f(x) = x|x|
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)