Advertisements
Advertisements
प्रश्न
Answer the following:
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5
उत्तर
f(x) = 5 – x for 0 ≤ x ≤ 4
f(x) = 5
∴ 5 – x = 5
∴ x = 0
APPEARS IN
संबंधित प्रश्न
find: f(1), f(−1), f(0) and f(2).
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}
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.
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
The function f is defined by \[f\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 3 \\ 3x, & 3 \leq x \leq 10\end{cases}\]
The relation g is defined by \[g\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 2 \\ 3x, & 2 \leq x \leq 10\end{cases}\]
Show that f is a function and g is not a function.
If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]
If for non-zero x, af(x) + bf \[\left( \frac{1}{x} \right) = \frac{1}{x} - 5\] , where a ≠ b, then find f(x).
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
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
The domain of definition of \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If f(m) = m2 − 3m + 1, find f(0)
Check if the relation given by the equation represents y as function of x:
x + y2 = 9
If f(m) = m2 − 3m + 1, find `f(1/2)`
If f(m) = m2 − 3m + 1, find f(− x)
Find the domain and range of the following function.
f(x) = 7x2 + 4x − 1
Express the area A of circle as a function of its radius r
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x2
Show that if f : A → B and g : B → C are onto, then g ° f is also onto
Express the following logarithmic equation in exponential form
log10 (0.001) = −3
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
Write the following expression as a single logarithm.
5 log x + 7 log y − log z
If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
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:
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:
If f(x) = 3x4 – 5x2 + 7 find f(x – 1)
Answer the following:
Simplify, log (log x4) – log (log x)
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 - x^2) + sqrt(5 - x)`
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Domain
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.
Find the range of the following functions given by `sqrt(16 - x^2)`
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Find the range of the following functions given by f(x) = `3/(2 - x^2)`
The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.
