Advertisements
Advertisements
प्रश्न
find: f(1), f(−1), f(0) and f(2).
उत्तर
f (1) = 4 × 1 + 1 = 5 [By using f (x) = 4x + 1, x > 0]
f ( -1) = 3 × (-1) -2 [By using f (x) = 3x -2, x < 0]
= -3-2=-5f (0) = 1 [By using f (x) = 1, x = 0]
f (2) = 4 × 2 + 1 [By using f (x) = 4x + 1, x > 0]
= 9
Hence,
f (1) = 5, f (- 1) = -5, f (0) = 1 and f (2) = 9.
APPEARS IN
संबंधित प्रश्न
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.
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
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:
(iii) f 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:
(vi) \[2f - \sqrt{5} g\]
Let f(x) = |x − 1|. Then,
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
Which of the following relations are functions? If it is a function determine its domain and range:
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Check if the following relation is a function.
Check if the following relation is a function.
Check if the relation given by the equation represents y as function of x:
x + y2 = 9
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Find the domain and range of the following function.
f(x) = 7x2 + 4x − 1
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Write the following expression as a single logarithm.
5 log x + 7 log y − log z
Write the following expression as a single logarithm.
ln (x + 2) + ln (x − 2) − 3 ln (x + 5)
Prove that logbm a = `1/"m" log_"b""a"`
Prove that alogcb = blogca
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:
A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist
Answer the following:
Find x, if x = 33log32
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy
Answer the following:
Find the domain of the following function.
f(x) = x!
Answer the following:
Find the range of the following function.
f(x) = |x – 5|
A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0
The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.
The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______
If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
If f(x) = `log_e{((1 - x))/((1 - x))}, |x| < 1, f{(2x)/((1 + x^2))}` is equal to ______.
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
Range of the function f(x) = `x/(1 + x^2)` is ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.