Advertisements
Advertisements
प्रश्न
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
पर्याय
(a) R
(b) R − {1}
(c) R − {−1/2, 1}
(d) None of these
उत्तर
(c) R − {−1/2, 1}
\[ \Rightarrow y = \frac{x(x - 1)}{x(x + 2)}\]
\[ \Rightarrow y = \frac{(x - 1)}{(x + 2)}\]
\[ \Rightarrow xy + 2y = x - 1\]
\[ \Rightarrow x = \frac{2y + 1}{1 - y}\]
\[\text{ Here } , 1 - y \neq 0 . \]
\[\text{ or } , y \neq 1 . \]
\[\text{ Also } , x \neq 0\]
\[ \Rightarrow \frac{2y + 1}{1 - y} \neq 0\]
\[ \Rightarrow y \neq - \frac{1}{2}\]
\[\text{ Thus, range } (f) = R - { - \frac{1}{2}, 1} . \]
APPEARS IN
संबंधित प्रश्न
If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
If \[f\left( x \right) = \frac{x - 1}{x + 1}\] , then show that
(i) \[f\left( \frac{1}{x} \right) = - f\left( x \right)\]
(ii) \[f\left( - \frac{1}{x} \right) = - \frac{1}{f\left( x \right)}\]
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(i) f + g
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(iii) f g
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
If f, g and h are real functions defined by
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is
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
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If f(m) = m2 − 3m + 1, find `f(1/2)`
A function f is defined as follows: f(x) = 4x + 5, for −4 ≤ x < 0. Find the values of f(−1), f(−2), f(0), if they exist.
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 1), (2, 1), (3, 1), (4, 1)}
If f(m) = m2 − 3m + 1, find f(0)
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
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(16 - x^2)`
Express the following exponential equation in logarithmic form
3–4 = `1/81`
The equation logx2 16 + log2x 64 = 3 has,
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
Select the correct answer from given alternatives
If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to
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:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
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?
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided 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 `|x - 4|/(x - 4)`
Find the range of the following functions given by `sqrt(16 - x^2)`
Find the domain of the following functions given by f(x) = x|x|
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
The ratio `(2^(log_2 1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.
