Advertisements
Advertisements
Question
Express the area A of a square as a function of its side s
Solution
If s is the side of the square, then area A is given by A = s2
APPEARS IN
RELATED QUESTIONS
find: f(1), f(−1), f(0) and f(2).
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].
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
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.
(b) f2 = {(1, 1), (2, 7), (3, 5)}
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
Check if the following relation is a function.
Check if the following relation is a function.
If f(m) = m2 − 3m + 1, find f(x + 1)
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x2
lf f(x) = 3(4x+1), find f(– 3)
Express the following exponential equation in logarithmic form
e–x = 6
Express the following logarithmic equation in exponential form
ln 1 = 0
Solve for x.
log2 x + log4 x + log16 x = `21/4`
The equation logx2 16 + log2x 64 = 3 has,
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:
If f(x) = 3x4 – 5x2 + 7 find f(x – 1)
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - 3) + 1/(log(5 - x))`
Answer the following:
Find the range of the following function.
f(x) = |x – 5|
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 |
Check if this relation is a function
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
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 7, 11, 16, 27, 31, 33, 42, 49 is ______.
If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
Find the domain of the following functions given by f(x) = x|x|
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.