Advertisements
Advertisements
प्रश्न
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
उत्तर
Let f(x) = y
y = `3/(2 - x^2)`
⇒ 2 – x2
= `3/"y"`
⇒ = `2 - 3/y`
But, we know that, x2 ≥ 0
`2 - 3/y ≥ 0`
⇒ `(2y - 3)/y ≥ 0`
⇒ y > 0 and 2y – 3 ≥ 0
⇒ y > 0 and 2y ≥ 3
⇒ y > 0 and y ≥ `3/2`
Or f(x) > 0 and f(x) ≥ `3/2`
f(x) ∈ `( – oo, 0) ∪ (3/2 , oo)`
⇒ f(x) ∈ `( – oo, 0) ∪ (3/2 , oo)`
Therefore, the range of f = `(-oo, 0) ∪ (3/2 , oo)`.
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
(c) whether f(xy) = f(x) : f(y) holds
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Let f(x) = |x − 1|. Then,
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
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 \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find `f(1/2)`
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one
Express the following exponential equation in logarithmic form
54° = 1
Express the following exponential equation in logarithmic form
e–x = 6
If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b
Solve for x.
log2 x + log4 x + log16 x = `21/4`
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
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:
Simplify, log (log x4) – log (log x)
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
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 Range
A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Find the range of the following functions given by `sqrt(16 - x^2)`
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
The period of the function
f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.
The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.
