Advertisements
Advertisements
Question
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
Solution
3x − 6 = 21
∴ x = `(21 + 6)/3` = 9
x = 9 represents a point on the X-axis.
There is no y involved in the equation.
So the given equation does not represent a function.
APPEARS IN
RELATED QUESTIONS
What is the fundamental difference between a relation and a function? Is every relation a function?
find: f(1), f(−1), f(0) and f(2).
Write the domain and range of \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.
If f : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for } - 2 \leq x \leq 0 \\ x - 1, & \text{ for } 0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
Check if the following relation is function:
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(3)
Which of the following relations are functions? 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)}
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(2)
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 2), (2, −1), (3, 1), (4, 3)}
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Find the domain and range of the following function.
f(x) = `sqrt((x - 3)/(7 - x))`
An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Solve for x.
log2 + log(x + 3) – log(3x – 5) = log3
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour
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 a and b
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Write an expression for gf(x) in its simplest form
The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______
The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Find the domain of the function f given by f(x) = `1/sqrt([x]^2 - [x] - 6)`
Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`
Find the range of the following functions given by f(x) = 1 – |x – 2|
Find the range of the following functions given by f(x) = |x − 3|
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The function f: R `rightarrow` R defined by f(x) = sin x is ______.