Advertisements
Advertisements
Question
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 ______.
Solution
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 {2, 8, 10}.
Explanation:
Since Domain of f = Df
= {2, 5, 8, 10}
And Domain of g = Dg
= {2, 7, 8, 10, 11}
Therefore the domain of f + g = {x | x ∈ Df ∩ Dg}
= {2, 8, 10}
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.
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
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:
(viii) \[\frac{5}{8}\]
If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]
The range of f(x) = cos [x], for π/2 < x < π/2 is
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
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 \[f\left( x \right) = \sqrt{4x - x^2}\] is
If \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Express the area A of circle as a function of its circumference C.
Write the following expression as sum or difference of logarithm
`log (sqrt(x) root(3)(y))`
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 2)}
Answer the following:
Find whether the following function is one-one
f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}
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, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - 3) + 1/(log(5 - x))`
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
A function f is defined by f(x) = 2x – 3 find x such that f(x) = x
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
The domain of the function f(x) = log3+x (x2 - 1) is ______.
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Find the range of the following functions given by f(x) = |x − 3|
Let f(x) = `sqrt(1 + x^2)`, then ______.
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.
