Advertisements
Advertisements
प्रश्न
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
पर्याय
(a) {(1, 2), (1, 3), (2, 3), (3, 3)}
(b) [(1, 3), (2, 4)]
(c) {(1, 3), (2, 2), (3, 3)}
(d) {(1, 2), (2, 3), (3, 2), (3, 4)}
उत्तर
(c) {(1, 3), (2, 2), (3, 3)}
We have
R = {(1, 3), (2, 2), (3, 3)}
We observe that each element of the given set has appeared as first component in one and only one ordered pair of R.
So, R = {(1, 3), (2, 2), (3, 3)} is a function.
APPEARS IN
संबंधित प्रश्न
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
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:
(ii) g − f
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:
(viii) \[\frac{5}{8}\]
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).
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
Which of the following are functions?
The domain of definition of the function \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find f(− x)
If f(m) = m2 − 3m + 1, find f(x + 1)
Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`
Find the domain and range of the following function.
f(x) = 7x2 + 4x − 1
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Write the following expression as sum or difference of logarithm
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
Write the following expression as a single logarithm.
5 log x + 7 log y − log z
Prove that alogcb = blogca
Answer the following:
Find whether the following function is one-one
f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}
Answer the following:
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5
Answer the following:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
Answer the following:
For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
Show that, logy x3 . logz y4 . logx z5 = 60
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) = 3 – 2x. Find x such that f(x2) = (f(x))2
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
The domain of the function f(x) = `sqrtx` is ______.
Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.
Find the range of the following functions given by `|x - 4|/(x - 4)`
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
