Advertisements
Advertisements
प्रश्न
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 2)}
उत्तर
{(12, 1), (3, 1), (5, 2)}
Every element of set A has been assigned a unique element in set B.
∴ Given relation is the function
Domain = {12, 3, 5}, Range = {1, 2}
APPEARS IN
संबंधित प्रश्न
If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 1))`
What is the fundamental difference between a relation and a function? Is every relation a function?
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If \[f\left( x \right) = \begin{cases}x^2 , & \text{ when } x < 0 \\ x, & \text{ when } 0 \leq x < 1 \\ \frac{1}{x}, & \text{ when } x \geq 1\end{cases}\]
find: (a) f(1/2), (b) f(−2), (c) f(1), (d)
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
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) \[\frac{5}{8}\]
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
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
Let f(x) = |x − 1|. Then,
The range of f(x) = cos [x], for π/2 < x < π/2 is
Which of the following are functions?
If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are
If \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
If f(m) = m2 − 3m + 1, find f(−3)
Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Find the domain and range of the following function.
f(x) = `sqrt((x - 3)/(7 - x))`
Express the area A of circle as a function of its diameter d
Express the following exponential equation in logarithmic form
25 = 32
Express the following exponential equation in logarithmic form
10−2 = 0.01
Prove that `"b"^(log_"b""a"` = a
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
Simplify `log_10 28/45 - log_10 35/324 + log_10 325/432 - log_10 13/15`
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`
A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(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 ______.
