Advertisements
Advertisements
Question
find: f(1), f(−1), f(0) and f(2).
Solution
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
RELATED QUESTIONS
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.
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
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:
(i) 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:
(ii) g − f
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, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge x, then write the value of (hogof)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
Which of the following are functions?
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
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 the function
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.
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
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 circle as a function of its radius r
Express the area A of circle as a function of its diameter d
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
25 = 32
Write the following expression as sum or difference of logarithm
`log (sqrt(x) root(3)(y))`
Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b
Prove that logbm a = `1/"m" log_"b""a"`
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 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:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Answer the following:
If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(x))`
Answer the following:
Find the range of the following function.
f(x) = [x] – x
Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
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 a and b
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
