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, 2), (2, −1), (3, 1), (4, 3)}
उत्तर
Let f = {(1, 2), (2, −1), (3, 1), (4, 3)}
f is a function because every element of A is related to one and only one element of B.
APPEARS IN
संबंधित प्रश्न
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.
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
If f, g and h are real functions defined by
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).
Write the domain and range of function f(x) given by
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\] is equal to
If \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) =
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
If \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find f(0)
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
Check if the following relation is a function.
Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2
Find the domain and range of the following function.
f(x) = `sqrt((x - 2)(5 - x)`
Find the domain and range of the following function.
f(x) = `sqrt(16 - x^2)`
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
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
Write the following expression as a single logarithm.
`1/3 log (x - 1) + 1/2 log (x)`
Solve for x.
log2 x + log4 x + log16 x = `21/4`
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
The equation logx2 16 + log2x 64 = 3 has,
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
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:
Simplify, log (log x4) – log (log x)
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
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
Find the domain of the following function.
f(x) = [x] + x
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 ______.
If f(x) = `(x - 1)/(x + 1)`, then show that `f(- 1/x) = (-1)/(f(x))`
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f is ______.