Advertisements
Advertisements
प्रश्न
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
उत्तर
f is a rational function of the form `(g(x))/(h(x))`
Where g(x) = x and h(x) = x2 + 3x + 2.
Now h(x) ≠ 0
⇒ x2 + 3x + 2 ≠ 0
⇒ (x + 1)(x + 2) ≠ 0
Hence domain of the given function is R – {– 1, – 2}.
APPEARS IN
संबंधित प्रश्न
Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.
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 f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}
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.
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (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(m) = m2 − 3m + 1, find f(− x)
A function f is defined as follows: f(x) = 4x + 5, for −4 ≤ x < 0. Find the values of f(−1), f(−2), f(0), if they exist.
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
Check if the relation given by the equation represents y as function of x:
x2 − y = 25
Express the following exponential equation in logarithmic form
e2 = 7.3890
Express the following logarithmic equation in exponential form
log10 (0.001) = −3
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"`
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:
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:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Find the height of a person whose forehand length is 40 cm
The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______
The domain of the function f(x) = log3+x (x2 - 1) is ______.
The range of the function y = `1/(2 - sin3x)` is ______.
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.
