Advertisements
Advertisements
प्रश्न
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
उत्तर
Let f = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
f is a function because every element of domain has only one image.
Domain of f = {2, 4, 6, 8, 10, 12, 14}
Range of f = {1, 2, 3, 4, 5, 6, 7}
APPEARS IN
संबंधित प्रश्न
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
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
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(0)
Check if the following relation is a function.
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)}
If f(m) = m2 − 3m + 1, find f(x + 1)
Find x, if g(x) = 0 where g(x) = 6x2 + x − 2
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
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 a square as a function of its perimeter P
Express the following exponential equation in logarithmic form
54° = 1
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
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:
Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3
Given the function f: x → x2 – 5x + 6, evaluate f(– 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?
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
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
The range of the function y = `1/(2 - sin3x)` is ______.
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.