Advertisements
Advertisements
प्रश्न
Let f and g be two real functions given by
f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}
Find the domain of fg.
उत्तर
It is given that f and g are two real functions such that
f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)}
and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}
Now,
Domain of f = Df = {0, 2, 3, 4, 5}
Domain of g = Dg = {1, 2, 3, 4, 5}
∴ Domain of fg = Df ∩ Dg = {2, 3, 4, 5}
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)}
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
What is the fundamental difference between a relation and a function? Is every relation a function?
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}
If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]
If f(x) = (x − a)2 (x − b)2, find f(a + b).
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:
(iii) f g
If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]
Write the domain and range of function f(x) given by
Let f and g be two functions given by
f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.
Find the domain of f + g
Which one of the following is not a function?
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,
The domain of definition of the function \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is
The domain of definition of the function f(x) = log |x| is
If f(m) = m2 − 3m + 1, find `f(1/2)`
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x3
Express the following exponential equation in logarithmic form
54° = 1
Express the following exponential equation in logarithmic form
e2 = 7.3890
Write the following expression as a single logarithm.
5 log x + 7 log y − log z
Prove that logbm a = `1/"m" log_"b""a"`
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
The equation logx2 16 + log2x 64 = 3 has,
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
Answer the following:
Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph
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)`
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
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 `("f"(0) + "f"(1))/2`
The domain of the function f(x) = log3+x (x2 - 1) is ______.
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
The domain of the function f defined by f(x) = `sqrt(4 - x) + 1/sqrt(x^2 - 1)` is equal to ______.
The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.
The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.