Advertisements
Advertisements
Question
Find the domain and range of the function f(x) = `1/sqrt(x - 5)`
Solution
Given that: f(x) = `1/sqrt(x - 5)`
Here, it is clear that f(x) is real when x – 5 > 0
⇒ x > 5
Hence, the domain = `(5, oo)`
Now to find the range put
f(x) = y = `1/sqrt(x - 5)`
⇒ `sqrt(x - 5) = 1/y`
⇒ `x - 5 = 1/y^2`
⇒ x = `1/y^2 + 5`
For x ∈ `(5, oo)`, y ∈ R+
Hence, the range of f = R+.
APPEARS IN
RELATED QUESTIONS
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.
et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.
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:
(v) \[\frac{g}{f}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),
Write the domain and range of \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
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
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} =
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 definition of \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
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)}
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(− x)
Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?
Prove that logbm a = `1/"m" log_"b""a"`
If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy
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 ______.
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
Answer the following:
If f(x) = 3x + a and f(1) = 7 find a and f(4)
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(x))`
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______
Find the range of the following functions given by f(x) = |x − 3|
Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3
The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval
