Advertisements
Advertisements
प्रश्न
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
उत्तर
2y + 10 = 0
∴ y = – 5
It is a constant function.
APPEARS IN
संबंधित प्रश्न
Define a function as a correspondence between two sets.
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
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(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 domain and range of function f(x) given by
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(x) =
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
The domain of definition of the function \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is
The domain of definition of the function f(x) = log |x| is
The range of the function f(x) = |x − 1| is
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
A function f is defined as follows: f(x) = 4x + 5, for −4 ≤ x < 0. Find the values of f(−1), f(−2), f(0), if they exist.
Check if the following relation is a function.
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x3
Find the domain of f(x) = ln (x − 5)
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 f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}
Answer the following:
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5
Answer the following:
Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not
Answer the following:
Find x, if x = 33log32
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3
Find the domain of the following function.
f(x) = `sqrtlog(x^2 - 6x + 6)`
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
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?
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
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
The domain of the function f(x) = `sqrtx` is ______.
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
Find the domain of the following function.
f(x) = [x] + x
Find the domain of the following function given by:
f(x) = `(3x)/(2x - 8)`
Let f(x) = `sqrt(1 + x^2)`, then ______.
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.