`f(x) = 1/(4x-1)` in `[1,4]`

Verify the hypothesis and conclusion of Lagrange's mean-value theorem for the function f(x) = (1)/((4 x -1)), 1 le x le 4

The function f(x) = [ 1/4(3x^2 + 1), -oo< x<= 1; 5-4x, 1 < x< 4; 4-x, 4 <=x < oo is

For f to be continuous at x = f(0) is given by {:("Column- I " , " Column - II"),("(A)" f(x) = (ln(1 +4x))/x, "(p)" 1/4),("(B)" f(x)=(ln(4+x)-ln4)/x , "(q) 0"),("(C)" f(x) = 1/sinx - 1/tan x , "(r)"4),("(D)" f(x)=(1-cos^(3)x)/( x sin 2x) , "(s)" 3/4):}

If f (x) =(x+3)/(4x-5) and t =(3+ 5x)/( 4x -1), then f (t) is

The function f(x)=(1)/(4)(3x^(2)+1) if -oo<=x<=1 and f(x)=5-4x if 1<=x<=4 and f(x)=4-x if 4<=x<=oo is:

" 4.If f(x)=(x+1)/(x-1) then f(x)+f((1)/(x)) is

If f(x)=cos^(-1)(4x^(3)-3x), x in [-1,1] , then

Let f : R to and f (x) = (x (x^(4) + 1) (x+1) +x ^(4)+2)/(x^(2) +x+1), then f (x) is :