Advertisements
Advertisements
Question
If f(x) = 3x + 5, g(x) = 6x − 1, then find `("f"/"g") (x)` and its domain
Solution
f(x) = 3x + 5, g(x) = 6x − 1
`("f"/"g") (x) = f(x)/g(x) = (3x + 5)/(6x - 1)`
`("f"/"g")(x)` is not defined if 6x − 1 = 0
i.e., if x = `1/6`
∴ Domain of `("f"/"g") = {x//x ∈ R, x ≠ 1/6}`
APPEARS IN
RELATED QUESTIONS
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(b) pre-images of 6, −3 and 5.
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
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:
(vii) f2 + 7f
Write the range of the function f(x) = ex−[x], x ∈ R.
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
If f(m) = m2 − 3m + 1, find f(−3)
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 2), (2, −1), (3, 1), (4, 3)}
Check if the relation given by the equation represents y as function of x:
x + y2 = 9
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Express the following exponential equation in logarithmic form
25 = 32
Express the following exponential equation in logarithmic form
3–4 = `1/81`
Express the following logarithmic equation in exponential form
log2 64 = 6
Write the following expression as a single logarithm.
ln (x + 2) + ln (x − 2) − 3 ln (x + 5)
Prove that `"b"^(log_"b""a"` = a
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f + g) (x)
Select the correct answer from given alternatives
The domain of `1/([x] - x)` where [x] is greatest integer function is
Answer the following:
A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1
Answer the following:
Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph
Answer the following:
Simplify `log_10 28/45 - log_10 35/324 + log_10 325/432 - log_10 13/15`
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Find the range of the following function.
f(x) = `x/(9 + x^2)`
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Find the height of a person whose forehand length is 40 cm
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
Domain of function f(x) = cos–1 6x is ______.
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) = |x − 3|
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.
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 ______.
