Advertisements
Advertisements
प्रश्न
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
उत्तर
f(x) = 3x + 5, g(x) = 6x − 1
f(2) = 3(2) + 5 = 11
g(2) = 6(2) - 1 = 11
∴ (f − g) (2) = f(2) − g(2)
= 11 − 11
= 0.
APPEARS IN
संबंधित प्रश्न
Find the domain of the function f(x) = `(x^2 + 2x + 1)/(x^2 - 8x + 12)`
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
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:
(v) \[\frac{g}{f}\]
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 : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
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 \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\] is equal to
If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are
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 \[f\left( x \right) = \sqrt{\frac{x - 2}{x + 2}} + \sqrt{\frac{1 - x}{1 + x}}\] is
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, 1), (2, 1), (3, 1), (4, 1)}
Express the area A of a square as a function of its side s
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
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
Answer the following:
Simplify, log (log x4) – log (log x)
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:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Given the function f: x → x2 – 5x + 6, evaluate f(– 1)
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Write an expression for gf(x) in its simplest form
The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.
The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
Find the domain of the following functions given by f(x) = x|x|
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)
Find the domain and range of the function f(x) = `1/sqrt(x - 5)`
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.
