Home
Class 12
MATHS
Let f:RtoR be a function defined as f(x)...

Let `f:RtoR` be a function defined as `f(x)={(5,"if", xle1),(a+bx,"if", 1ltxlt3),(b+5x,"if",3lexlt3),(30,"if",xge5):}` Then f is :

A

continuous if `a=-5` and b=10

B

continuous if `a=0` and `b=5`

C

not continuous for nay value of a and b

D

continuous if a=5 and b=5

Text Solution

Verified by Experts

The correct Answer is:
C
The function is continuous at `x=1` if `a+b=5` at `x=3` if `a+3b=b+15` and at `x=5` if `b+25=30`. Clearly the three equations in a and b are inconsistent.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f:R to R be a function defined as f(x)={{:(5,"if" x le 1),(a+bx , "if" 1 lt x lt 3),(b+5x , "if" 3 le x lt 5),(30 , "if" x ge 5):} then f is

Let f:R to R be a function defined b f(x)=cos(5x+2). Then,f is

Let f: RtoR be function defined by f(x)=sin (2x-3) , then f is

Let f:R rarr R be the function defined by f(x)=x^(3)+5 then f^(-1)(x) is

Let f(x) be a function defined as f(x)={{:(sin(x^2-3x)", "xle0),(6x+5x^2", "xgt0):} Then at x=0,f(x)

Let a function f : R to R be defined as f(x)={{:(sinx-e^(x),if,xle0),(a+[-x],if,0ltxlt1),(2x-b,if,xge1):} Where [x] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:

Find the value of 'a' and 'b' such that the function defined by : f(x)={{:(5", if "xle2),(ax+b", if "2ltxlt5),(20", if "xge5):} is a continuous function.

Let f:RtoR be a function whose inverse is (x+5)/(3) . What is f(x) equal to?