Advertisements
Advertisements
प्रश्न
Answer the following:
If f(x) = 3x + a and f(1) = 7 find a and f(4)
उत्तर
f(x) = 3x + a
∴ f(1) = 3(1) + a = 3 + a
∴ f(1) = 7 gives
3 + a = 7
∴ a = 4
∴ f(x) = 3x + 4
∴ f(4) = 3(4) + 4 = 16.
APPEARS IN
संबंधित प्रश्न
Find the domain of the function f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`
Define a function as a correspondence between two sets.
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
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:
(iii) f g
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 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)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .
Let f(x) = |x − 1|. Then,
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and} g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to
If \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,
The domain of definition of the function \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is
Check if the relation given by the equation represents y as function of x:
x + y2 = 9
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
If f(m) = m2 − 3m + 1, find `f(1/2)`
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
An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain
Solve for x.
log2 x + log4 x + log16 x = `21/4`
Solve for x.
x + log10 (1 + 2x) = x log10 5 + log10 6
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
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:
Find the domain of the following function.
f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Describe the following Range
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
Domain of function f(x) = cos–1 6x is ______.
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
Find the range of the following functions given by `|x - 4|/(x - 4)`
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^3 - x + 3)/(x^2 - 1)`
Let f(x) = `sqrt(1 + x^2)`, then ______.
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.
Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.
