Advertisements
Advertisements
Question
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 2)}
Solution
{(12, 1), (3, 1), (5, 2)}
Every element of set A has been assigned a unique element in set B.
∴ Given relation is the function
Domain = {12, 3, 5}, Range = {1, 2}
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:
(a) range of f, i.e. f(A).
find: f(1), f(−1), f(0) and f(2).
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
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:
(vii) f2 + 7f
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
Let \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] . Then write the value of α satisfying f(f(x)) = x for all x ≠ −1.
Write the domain and range of function f(x) given by
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
If f(x) = cos (log x), then the value of f(x) f(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is
Which of the following are functions?
Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =
If f(m) = m2 − 3m + 1, find f(−3)
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = 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)}
If f(m) = m2 − 3m + 1, find f(x + 1)
Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one
Express the following logarithmic equation in exponential form
ln 1 = 0
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
Solve for x.
x + log10 (1 + 2x) = x log10 5 + log10 6
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Answer the following:
Find x, if x = 33log32
Answer the following:
If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy
Answer the following:
Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
A graph representing the function f(x) is given in it is clear that f(9) = 2
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Domain of function f(x) = cos–1 6x is ______.
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
Find the range of the following functions given by `|x - 4|/(x - 4)`
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`
The range of the function y = `1/(2 - sin3x)` is ______.
The range of the function f(x) = x2 + 2x+ 2 is ______.
