Advertisements
Advertisements
प्रश्न
If f(x) = 3x + 5, g(x) = 6x − 1, then find `("f"/"g") (x)` and its domain
उत्तर
f(x) = 3x + 5, g(x) = 6x − 1
`("f"/"g") (x) = f(x)/g(x) = (3x + 5)/(6x - 1)`
`("f"/"g")(x)` is not defined if 6x − 1 = 0
i.e., if x = `1/6`
∴ Domain of `("f"/"g") = {x//x ∈ R, x ≠ 1/6}`
APPEARS IN
संबंधित प्रश्न
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 \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
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 the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is
The domain of definition of the function f(x) = log |x| is
The range of the function f(x) = |x − 1| is
Which of the following relations are functions? If it is a function determine its domain and range:
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(0)
Check if the following relation is a function.
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
Express the following exponential equation in logarithmic form
54° = 1
Express the following exponential equation in logarithmic form
3–4 = `1/81`
Write the following expression as a single logarithm.
`1/3 log (x - 1) + 1/2 log (x)`
Prove that alogcb = blogca
If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)
Select the correct answer from given alternatives.
If log10(log10(log10x)) = 0 then x =
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:
Let f: R → R be a function defined by f(x) = 5x3 – 8 for all x ∈ R, show that f is one-one and onto. Hence find f –1
Answer the following:
A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1
Answer the following:
A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist
Answer the following:
Find x, if x = 33log32
Answer the following:
Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3
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 – 5|
Given the function f: x → x2 – 5x + 6, evaluate f(2)
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 function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
Find the domain of the following function.
f(x) = [x] + x
Find the range of the following functions given by `|x - 4|/(x - 4)`
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Find the range of the following functions given by f(x) = |x − 3|
The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.
The ratio `(2^(log_2 1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.
The period of the function
f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.
