Advertisements
Advertisements
प्रश्न
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
पर्याय
(a) 1
(b) 2
(c) 3
(d) 4
उत्तर
(c) 3 \[f\left( x \right) = \frac{x + 1}{x - 1}\] \[f(f(f(2))) \]
\[ = f\left( f\left( \frac{2 + 1}{2 - 1} \right) \right)\]
\[ = f\left( f(3) \right)\]
\[ = f\left( \frac{3 + 1}{3 - 1} \right)\]
\[ = f(2) = 3\]
APPEARS IN
संबंधित प्रश्न
What is the fundamental difference between a relation and a function? Is every relation a function?
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(b) {x : f(x) = −2}
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
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
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:
(vi) \[2f - \sqrt{5} g\]
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
The range of f(x) = cos [x], for π/2 < x < π/2 is
If f : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for } - 2 \leq x \leq 0 \\ x - 1, & \text{ for } 0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =
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 \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then
If f(m) = m2 − 3m + 1, find f(−3)
If ƒ(m) = m2 − 3m + 1, find f(x + 1)
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(3)
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
Check if the following relation is a function.
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
Find the domain and range of the following function.
f(x) = `sqrt((x - 3)/(7 - x))`
Find the domain and range of the following function.
f(x) = `sqrt(16 - x^2)`
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x3
Express the following exponential equation in logarithmic form
231 = 23
Express the following exponential equation in logarithmic form
e–x = 6
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
If f(x) = 3x4 – 5x2 + 7 find f(x – 1)
Answer the following:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
Find the domain of the following function.
f(x) = `sqrtlog(x^2 - 6x + 6)`
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
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 f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
If f(x) = 5x - 3, then f-1(x) is ______
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
Find the range of the following functions given by `sqrt(16 - x^2)`
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`
Find the range of the following functions given by f(x) = |x − 3|
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f is ______.
