Advertisements
Advertisements
प्रश्न
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
उत्तर
(c) Given:
f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
f3 is not a function from X to Y because 2 ∈ X has two images, 9 and 11, in Y.
APPEARS IN
संबंधित प्रश्न
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
Define a function as a correspondence between two sets.
What is the fundamental difference between a relation and a function? Is every relation a function?
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(b) f2 = {(1, 1), (2, 7), (3, 5)}
Write the range of the real function f(x) = |x|.
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 range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
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.
If f(x) = 4x − x2, x ∈ R, then write the value of f(a + 1) −f(a − 1).
If f(x) = cos (log x), then the value of f(x2) f(y2) −
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(x) = log |x| is
Check if the following relation is a function.
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
Express the area A of a square as a function of its side s
Express the area A of circle as a function of its circumference C.
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x2
Express the following logarithmic equation in exponential form
log2 64 = 6
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.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Select the correct answer from given alternative.
The domain and range of f(x) = 2 − |x − 5| is
Answer the following:
Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph
Answer the following:
Simplify `log_10 28/45 - log_10 35/324 + log_10 325/432 - log_10 13/15`
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - 3) + 1/(log(5 - x))`
Answer the following:
Find the range of the following function.
f(x) = [x] – x
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
For what value of x is f(x) = 1?
Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Check if this relation is a function
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
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 ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
The ratio `(2^(log_2 1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.
