Advertisements
Advertisements
प्रश्न
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
उत्तर
f : Z → Z given by f(x) = x2
f(2) = 22 = 4 and f(– 2) = (– 2)2 = 4
∴ f(2) = f(– 2) but 2 ≠ – 2
∴ f is not injective
2 ∈ Z but there is no x ∈ Z such that 2 = f(x) = x2
∴ f is not surjective
∴ f is neither injective nor surjective.
APPEARS IN
संबंधित प्रश्न
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(b) pre-images of 6, −3 and 5.
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
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
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) \[\frac{5}{8}\]
Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (f + g) (x), (f − g) (x), (fg) (x) and \[\left( \frac{f}{g} \right) \left( x \right)\] .
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
Write the range of the function f(x) = ex−[x], x ∈ R.
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
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 the function \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`
Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x3
Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one
Express the following exponential equation in logarithmic form
`9^(3/2)` = 27
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Solve for x.
log2 + log(x + 3) – log(3x – 5) = log3
Solve for x.
2 log10 x = `1 + log_10 (x + 11/10)`
Solve for x.
log2 x + log4 x + log16 x = `21/4`
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
If f(x) = 3x + 5, g(x) = 6x − 1, then find `("f"/"g") (x)` and its domain
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:
Let f : R → R be given by f(x) = x3 + 1 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:
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
An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of 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 |
Find the height of a person whose forehand length is 40 cm
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 for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.
Find the range of the following functions given by f(x) = |x − 3|
Which of the following functions is NOT one-one?
Range of the function f(x) = `x/(1 + x^2)` is ______.
