`f(x)={4x-x^3+ln(a^2-3a+3),0lt=x<3x-18 ,xgeq3` complete set of values of `a` such that `f(x)` as a local minima at `x=3` is `[-1,2]` `(-oo,1)uu(2,oo)` `[1,2]` (d) `(-oo,-1)uu(2,oo)`

Find the values of 'a' for which, f(x)={(4x-x^(3)+log(a^(2)-3a+3)",",0lexlt3),(" "x-18",",xge3):} , f(x) as a local minima at x=3 is

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} . Describe the function f//g and find its domain.

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

f(x)=log_(3)(5+4x-x^(2))

If f(x)={{:(,4,-3lt x lt -1),(,5+x,-1le x lt 0),(,5-x,0 le x lt 2),(,x^(2)+x-3,2 lt x lt 3):} then, f(|x|) is

The relation f is defined by f(x)={x^2,""0lt=xlt=3 3x ,""""3lt=xlt=10 The relating g is defined by g(x)={x^2,""0lt=xlt=3 3x ,""""2lt=xlt=10 Show that f is a function and g is not a function.

The value of a for which the function f(x)=f(x)={((4^x-1)hat3)/(sin(x a)log{(1+x^2 3)}),x!=0 12(log4)^3,x=0 may be continuous at x=0 is 1 (b) 2 (c) 3 (d) none of these

Number of points where f (x)= {{:(max(|x ^(2)- x-2","x ^(2) -3x),,, x ge0),( max (ln (-x)"," e ^(x)),,, x lt 0):} is non-differentiable will be:

If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):} , then g(x) = f(|x|) is

f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3):}