Advertisements
Advertisements
प्रश्न
Check if the following relation is a function.
उत्तर
No
Reason:
An element of set A has been assigned more than one element from set B.
APPEARS IN
संबंधित प्रश्न
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that 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:
(iii) f g
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:
(v) \[\frac{g}{f}\]
Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (f + g) (x), (f − g) (x), (fg) (x) and \[\left( \frac{f}{g} \right) \left( x \right)\] .
Let f and g be two functions given by
f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.
Find the domain of f + g
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and} g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to
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
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
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 f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
Which of the following relations are functions? If it is a function determine its domain and range:
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
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.
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
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(16 - x^2)`
Express the following exponential equation in logarithmic form
`"e"^(1/2)` = 1.6487
Write the following expression as sum or difference of logarithm
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)
The equation logx2 16 + log2x 64 = 3 has,
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
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) = |x – 5|
A graph representing the function f(x) is given in it is clear that f(9) = 2
What is the image of 6 under f?
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
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Find the domain of the function f given by f(x) = `1/sqrt([x]^2 - [x] - 6)`
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 ______.
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Find the range of the following functions given by f(x) = 1 + 3 cos2x
(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)
If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.
lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f is ______.