Advertisements
Advertisements
प्रश्न
Answer the following:
Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph
उत्तर
Let y = f(x) = x3 + 1
x | –2 | –1 | 0 | 1 | 2 |
y | –7 | 0 | 1 | 2 | 9 |
APPEARS IN
संबंधित प्रश्न
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
- {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
- {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
- {(1, 3), (1, 5), (2, 5)}
If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 1))`
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
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 \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
Write the range of the function f(x) = ex−[x], x ∈ R.
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
If f(x) = 4x − x2, x ∈ R, then write the value of f(a + 1) −f(a − 1).
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)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
Which one of the following is not a function?
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
The domain of the function
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If ƒ(m) = m2 − 3m + 1, find f(x + 1)
Which of the following relations are functions? 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)}
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
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
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 : R → R given by f(x) = x3
lf f(x) = 3(4x+1), find f(– 3)
Express the following exponential equation in logarithmic form
54° = 1
Express the following exponential equation in logarithmic form
231 = 23
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Solve for x.
x + log10 (1 + 2x) = x log10 5 + log10 6
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Answer the following:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
A graph representing the function f(x) is given in it is clear that f(9) = 2
What is the image of 6 under f?
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Write an expression for gf(x) in its simplest form
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.