English

Check if the relation given by the equation represents y as function of x: 2y + 10 = 0 - Mathematics and Statistics

Advertisements
Advertisements

Question

Check if the relation given by the equation represents y as function of x:

2y + 10 = 0

Sum

Solution

2y + 10 = 0

∴ y = – 5

It is a constant function.

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Functions - Exercise 6.1 [Page 118]

RELATED QUESTIONS

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

  1. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
  2. {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
  3. {(1, 3), (1, 5), (2, 5)}

Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.


et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.


If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].

 

If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]


If  \[f\left( x \right) = \begin{cases}x^2 , & \text{ when }  x < 0 \\ x, & \text{ when }  0 \leq x < 1 \\ \frac{1}{x}, & \text{ when }  x \geq 1\end{cases}\]

find: (a) f(1/2), (b) f(−2), (c) f(1), (d)

\[f\left( \sqrt{3} \right)\] and (e) \[f\left( \sqrt{- 3} \right)\]
 

If f(x) = loge (1 − x) and g(x) = [x], then determine function:

(ii) fg


If f(x) = cos (log x), then the value of f(x2f(y2) −

\[\frac{1}{2}\left\{ f\left( \frac{x^2}{y^2} \right) + f\left( x^2 y^2 \right) \right\}\] is
 

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 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to

 

Let f : R → R be defined by f(x) = 2x + |x|. Then f(2x) + f(−x) − f(x) =


If f(m) = m2 − 3m + 1, find `f(1/2)`


Find x, if g(x) = 0 where g(x) = `(18 -2x^2)/7`


Find the domain and range of the following function.

f(x) = `sqrt((x - 3)/(7 - x))`


Express the area A of a square as a function of its perimeter P


Express the area A of circle as a function of its diameter d


Express the following exponential equation in logarithmic form

25 = 32


Express the following logarithmic equation in exponential form

ln e = 1


Write the following expression as a single logarithm.

ln (x + 2) + ln (x − 2) − 3 ln (x + 5)


Prove that logbm a = `1/"m" log_"b""a"`


Solve for x.

log2 + log(x + 3) – log(3x – 5) = log3


If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7


If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy 


Answer the following:

For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3


Answer the following:

If `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b


Answer the following:

If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy


Answer the following:

If f(x) = log(1 – x), 0 ≤ x < 1 show that `"f"(1/(1 + x))` = f(1 – x) – f(– x)


Given the function f: x → x2 – 5x + 6, evaluate f(– 1)


A graph representing the function f(x) is given in it is clear that f(9) = 2

For what value of x is f(x) = 1?


An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x


The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` 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 domain of the following functions given by f(x) = `1/sqrt(x + |x|)`


Find the domain of the following function given by:

f(x) = `(3x)/(2x - 8)`


If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)


If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.


The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×