If `f(x)={(|x|-3` when ` x < 1)`, and `(|x-2|+a ,` when `x >= 1)` &
`g(x)={2-|x| `when ` x < 2` and `sgn(x)-b` , when `x >= 2`.
if `h(x)=f(x)+g(x)` is discontinuous at exactly one point, then -
(a). `a=-3, b=0`
(b). `a=-3, b=-1 `
(c) `a=2, b=1`
(d) `a=0, b=1`

Given , f(x)={{:((1-cos3x)/(x^(2)),"when " xne0),(1,"when "x=0):} Prove that f (x) is discontinuous at x = 0 .

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

f(x)={(x-1, -1lexlt0),(x^2, 0ltxle1):} and g(x)=sin x. Then find h(x)=f(|g(x)|)+|f(g(x))|

f(x)=x^2+ax ,when 0lexle1 and f(x)=3-bx^2 ,when 1lexle2 if limxrarr1f(x)=4 ,then find the value of a and b.

If f(x) =2x-1 and g(x)=3x+2 then find (fog) (x) a)2(3x+1) b)2(3x+2) c)(2x+1) d)3(3x+1)

If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x^3)/(x^2))^(1/x),x >0 is continuous at x=0, then a=0 b. b=e^3 c. a=1 d. b=(log)_e3

f is a continous function in [a, b] ; g is a continuous function in [b,c]. A function h(x) is defined as h(x)=f(x) for x in [a,b) , g(x) for x in (b,c] if f(b) =g(b) then (A) h(x) has a removable discontinuity at x = b. (B) h(x) may or may not be continuous in [a, c] (C) h(b-) = g(b+ ) and h(b+ ) = f(b- ) (D) h(b+ ) = g(b- ) and h(b- ) = f(b+ )

Let f(x)={1+(2x)/a ,0lt=x 1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

If f(x)={{:("2x+3, when x is an rational ,"),(x^(2)+1", when x is irrational,"):} then f(0) =