Advertisements
Advertisements
प्रश्न
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)}
उत्तर
{(1, 3), (4, 1), (2, 2)} does not represent a function.
Reason:
3 ∈ A does not have an image in set B.
APPEARS IN
संबंधित प्रश्न
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, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(b) {x : f(x) = −2}
If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]
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
Write the domain and range of function f(x) given by
If f(x) = cos (log x), then the value of f(x2) f(y2) −
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
Let f(x) = |x − 1|. Then,
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find f(− x)
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
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, 2), (2, −1), (3, 1), (4, 3)}
Check if the relation given by the equation represents y as function of x:
x2 − y = 25
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Express the area A of a square as a function of its perimeter P
Express the following logarithmic equation in exponential form
log2 64 = 6
Express the following logarithmic equation in exponential form
In `1/2` = – 0.693
Find the domain of f(x) = log10 (x2 − 5x + 6)
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}
Answer the following:
Find x, if x = 33log32
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Find the domain of the following function.
f(x) = `sqrtlog(x^2 - 6x + 6)`
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
A function f is defined by f(x) = 2x – 3 find x such that f(x) = x
A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Find the range of the following functions given by `sqrt(16 - x^2)`
Find the domain of the function f given by f(x) = `1/sqrt([x]^2 - [x] - 6)`
Find the range of the following functions given by f(x) = 1 + 3 cos2x
(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)
Range of f(x) = `1/(1 - 2 cosx)` is ______.