Advertisements
Advertisements
प्रश्न
Find x, if g(x) = 0 where g(x) = 6x2 + x − 2
उत्तर
g(x) = 0
∴ 6x2 + x – 2 = 0
∴ (3x + 2)(2x – 1) = 0
∴ 3x + 2 = 0 or 2x – 1 = 0
∴ x = `-2/3` or x = `1/2`
APPEARS IN
संबंधित प्रश्न
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(a) range of f, i.e. f(A).
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}
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(c) whether f(xy) = f(x) : f(y) holds
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),
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).
Write the domain and range of function f(x) given by
Write the domain and range of \[f\left( x \right) = \sqrt{x - \left[ x \right]}\] .
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
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 : [−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 f(m) = m2 − 3m + 1, find `f(1/2)`
If ƒ(m) = m2 − 3m + 1, find f(x + 1)
Which of the following relations are functions? If it is a function determine its domain and range:
{(0, 0), (1, 1), (1, −1), (4, 2), (4, −2), (9, 3), (9, −3), (16, 4), (16, −4)}
If f(x) = 3x + a and f(1) = 7 find a and f(4).
Check if the following relation is a function.
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Express the area A of a square as a function of its side s
Express the following exponential equation in logarithmic form
10−2 = 0.01
Express the following logarithmic equation in exponential form
log2 64 = 6
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Write the following expression as a single logarithm.
ln (x + 2) + ln (x − 2) − 3 ln (x + 5)
If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy
The equation logx2 16 + log2x 64 = 3 has,
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
Answer the following:
Let f : R → R be given by f(x) = x + 5 for all x ∈ R. Draw its graph
Answer the following:
If b2 = ac. prove that, log a + log c = 2 log b
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Answer the following:
Find the range of the following function.
f(x) = [x] – x
Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?
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
What is the image of 6 under f?
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
If f(x) = `(x - 1)/(x + 1)`, then show that `f(- 1/x) = (-1)/(f(x))`
If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.