Advertisements
Advertisements
प्रश्न
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
उत्तर
(iii) Given:
h (x) = x2 + 1
Range of h (x) = {y ∈ R : y ≥ 1}
APPEARS IN
संबंधित प्रश्न
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 : 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 A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a 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:
(v) \[\frac{g}{f}\]
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) \[2f - \sqrt{5} g\]
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:
(vii) f2 + 7f
Write the range of the real function f(x) = |x|.
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
f is a real valued function given by \[f\left( x \right) = 27 x^3 + \frac{1}{x^3}\] and α, β are roots of \[3x + \frac{1}{x} = 12\] . Then,
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 the function f(x) = log |x| is
The domain of definition of \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(0)
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Express the area A of a square as a function of its side s
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?
Express the following exponential equation in logarithmic form
e2 = 7.3890
Write the following expression as a single logarithm.
ln (x + 2) + ln (x − 2) − 3 ln (x + 5)
If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Select the correct answer from given alternatives.
If f : R → R is defined by f(x) = x3 then f–1 (8) is equal to :
Answer the following:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`
A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0
An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x
A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour
If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find `(f/g)(x)`
The range of the function f(x) = x2 + 2x+ 2 is ______.
