Advertisements
Advertisements
प्रश्न
Answer the following:
Find the domain of the following function.
f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`
उत्तर
f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`
= `(x + 2)^2/((x + 3)(x - 2))`
f(x) is not defined if (x + 3) (x – 2) = 0,
i.e., if x = – 3 or x = 2
∴ Domain = R – {2, – 3}
APPEARS IN
संबंधित प्रश्न
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
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:
(iii) \[\frac{f}{g}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
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 the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
If f, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge x, then write the value of (hogof)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
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.
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
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,
The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
The range of the function f(x) = |x − 1| is
If f(x) = 3x + a and f(1) = 7 find a and f(4).
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:
2x + 3y = 12
Express the area A of circle as a function of its radius r
Write the following expression as a single logarithm.
`1/3 log (x - 1) + 1/2 log (x)`
Prove that alogcb = blogca
If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Answer the following:
If f(x) = 3x + a and f(1) = 7 find a and f(4)
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:
Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
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
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
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 ______.