Advertisements
Advertisements
प्रश्न
If f, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge x, then write the value of (hogof)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
उत्तर
Given : f(x) = x2, g(x) = tan x and h(x) = loge x.
(hogof) \[\left( \sqrt{\frac{\pi}{4}} \right)\] = \[h\left( g\left( f\left( \sqrt{\frac{\pi}{4}} \right) \right) \right)\]
\[= h\left( g\left( \left( \sqrt{\frac{\pi}{4}} \right)^2 \right) \right)\]
\[ = h\left( g\left( \frac{\pi}{4} \right) \right)\]
\[ = h\left( \tan \left( \frac{\pi}{4} \right) \right)\]
\[ = h\left( 1 \right)\]
\[ = \log_e 1 = 0\]
APPEARS IN
संबंधित प्रश्न
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
f, g, h are three function defined from R to R as follow:
(ii) g(x) = sin x
Find the range of function.
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
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:
(iv) \[\frac{f}{g}\]
Write the domain and range of \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
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 \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If f(m) = m2 − 3m + 1, find f(0)
A function f is defined as follows: f(x) = 5 − x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 3), (4, 1), (2, 2)}
If f(m) = m2 − 3m + 1, find f(0)
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Express the area A of circle as a function of its radius r
lf f(x) = 3(4x+1), find f(– 3)
Express the following logarithmic equation in exponential form
log2 64 = 6
Write the following expression as a single logarithm.
ln (x + 2) + ln (x − 2) − 3 ln (x + 5)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(0, 0), (1, 1), (1, –1), (4, 2), (4, –2), (9, 3), (9, –3), (16, 4), (16, –4)}
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
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, logy x3 . logz y4 . logx z5 = 60
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(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
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 |
Find the height of a person whose forehand length is 40 cm
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Domain of function f(x) = cos–1 6x is ______.
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
