Advertisements
Advertisements
प्रश्न
If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]
उत्तर
Given: \[f\left( x \right) = 1 - \frac{1}{x}\]
Now, \[f\left( \frac{1}{x} \right) = 1 - \frac{1}{\frac{1}{x}} = 1 - x\]
If \[f\left( x \right) = 1 - \frac{1}{x}\]
\[ = \frac{- x}{1 - x}\]
\[ = \frac{- x}{- \left( x - 1 \right)}\]
\[ = \frac{x}{x - 1}\]
APPEARS IN
संबंधित प्रश्न
Define a function as a correspondence between two sets.
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(b) pre-images of 6, −3 and 5.
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
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:
(iv) \[\frac{f}{g}\]
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to
Check if the following relation is function:
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 following relation is a function.
Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x3
Express the following logarithmic equation in exponential form
In `1/2` = – 0.693
Find the domain of f(x) = log10 (x2 − 5x + 6)
If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7
If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 2)}
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 the range of the following function.
f(x) = `x/(9 + x^2)`
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Check if this relation is a function
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
Domain of function f(x) = cos–1 6x is ______.
Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.
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 range of the following functions given by f(x) = 1 – |x – 2|
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f – g)(x)
Range of f(x) = `1/(1 - 2 cosx)` is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
The range of the function f(x) = x2 + 2x+ 2 is ______.
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.
