Advertisements
Advertisements
प्रश्न
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
विकल्प
(a) R1 = [(p, 1), (q, 2), (r, 1), (s, 2)]
(b) R2 = [(p, 1), (q, 1), (r, 1), (s, 1)]
(c) R3 = [(p, 1), (q, 2), (p, 2), (s, 3)
(d) R4 = [(p, 2), (q, 3), (r, 2), (s, 2)].
उत्तर
(c) R3 = [(p, 1), (q, 2), (p, 2), (s, 3)
All the relations in (a), (b) and (d) have a unique image in B for all the elements in A.
R3 is not a function from A to B because p ∈ A has two images, 1 and 2, in B.
Hence, option (c) is not a function.
APPEARS IN
संबंधित प्रश्न
Define a function as a correspondence between two sets.
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
If f(x) = (a − xn)1/n, a > 0 and n ∈ N, then prove that f(f(x)) = x for all x.
Write the range of the function f(x) = ex−[x], x ∈ R.
Which of the following are functions?
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
The domain of definition of the function \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2
Express the area A of a square as a function of its perimeter P
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x2
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x3
If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
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:
For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
Simplify, log (log x4) – log (log x)
Answer the following:
If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)
Answer the following:
Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
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) = 1 + 2x + 4x
Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Write an expression for gf(x) in its simplest form
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
Find the range of the following functions given by f(x) = |x − 3|
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
The ratio `(2^(log_2 1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.
