Advertisements
Advertisements
प्रश्न
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
पर्याय
Domain = `(1, oo)`, Range = `(0, oo)`
Domain = `[1, oo)`, Range = `(0, oo)`
Domain = `[1, oo)`, Range = `[0, oo)`
Domain = `[1, oo)`, Range = `[0, oo)`
उत्तर
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by Domain = `[1, oo)`, Range = `[0, oo)`.
Explanation:
Given that: f(x) = `sqrt(x - 1)`
f(x) is defined if x – 1 ≥ 0
⇒ x ≥ 1
∴ Domain of f(x) = `[0, oo)`
Let f(x) = y = `sqrt(x - 1)`
⇒ y2 = x – 1
⇒ x = y2 + 1
If x is real then y ∈ R
∴ Range of f(x) = `[0, oo)`
APPEARS IN
संबंधित प्रश्न
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
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 A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
Check if the following relation is function:
Which of the following relations are functions? If it is a function determine its domain and range:
{(1, 1), (3, 1), (5, 2)}
Check if the following relation is a function.
If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`
Find the domain and range of the following function.
f(x) = `sqrt((x - 2)(5 - x)`
Express the area A of a square as a function of its perimeter P
Find the domain of f(x) = ln (x − 5)
Write the following expression as sum or difference of logarithm
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
Solve for x.
x + log10 (1 + 2x) = x log10 5 + log10 6
The equation logx2 16 + log2x 64 = 3 has,
Answer the following:
Let f: R → R be a function defined by f(x) = 5x3 – 8 for all x ∈ R, show that f is one-one and onto. Hence find f –1
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
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:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
Simplify, log (log x4) – log (log x)
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 function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
If f(x) = 5x - 3, then f-1(x) is ______
Find the range of the following functions given by `|x - 4|/(x - 4)`
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)
The ratio `(2^(log_2 1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.
