Advertisements
Advertisements
प्रश्न
If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 1))`
उत्तर
`f(x)=x^2`
`therefore(f(1.1)-f(1))/(1.1-1)=((1.1)^2-(1)^2)/(1.1-1)=(1.21-1)/0.1=0.21/0.1=2.1`
APPEARS IN
संबंधित प्रश्न
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].
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
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)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
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 : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for } - 2 \leq x \leq 0 \\ x - 1, & \text{ for } 0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
Check if the following relation is function:
Check if the following relation is a function.
Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`
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 : R → R given by f(x) = x3
Express the following exponential equation in logarithmic form
10−2 = 0.01
Express the following exponential equation in logarithmic form
e2 = 7.3890
Express the following exponential equation in logarithmic form
`"e"^(1/2)` = 1.6487
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Write the following expression as sum or difference of logarithm
`log (sqrt(x) root(3)(y))`
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"`
Prove that alogcb = blogca
Select the correct answer from given alternatives.
If log10(log10(log10x)) = 0 then x =
Select the correct answer from given alternatives
If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 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:
Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
A graph representing the function f(x) is given in it is clear that f(9) = 2
For what value of x is f(x) = 1?
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
Find the range of the following functions given by `|x - 4|/(x - 4)`
Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`
Find the range of the following functions given by f(x) = 1 – |x – 2|
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find `(f/g)(x)`
If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.
Which of the following functions is NOT one-one?