If `f(x) = {:|(a,-1,0),(ax,a,-1),(ax^2,ax,a)|`, using properties of determinants, find the value of `f(2x)-f(x)`

If f(x)=x^2 then find the value of (f(1.1)-f(1))/(1.1-1) .

If f (x) = |x|+|x-1|, find the value of : f(2).

If f (x) = |x|+|x-1|, find the value of : f(0).

Suppose f(x) is a function satisfying the folowing conditions: (i)f(0)=2,f(1)=1 (ii) f(x) has a minimum value at x=(5)/(2) (iii) for all xf'(x)= |{:(2ax,2ax-1,2ax+b+1),(b,b+1,-1),(2(ax+b),2ax+2b+1,2ax+b):}| The number of solutions of the equation f(x) +1=0 is

If the function f(x) given by: f(x) = {:{(2ax+b,ifx>1),(9,ifx=1),(6ax-2b,ifx<1):} is continuous at x =1, find the values 'a' and 'b'.

if f(x) = {{:(x^2, x le 1),(ax + b ,x gt 1):} is differentiable at x = 1 . Find the values of a and b.

If the function f(x) = {:{(3ax + b, if x > 1),(11, if x = 1),(5ax - 2b, if x < 1):} is continuous at x = 1, find the values of a,b.

f(x)+f(1-1/x)=1+x for x in R-{0,1}. Find the value of 4f(2).

Suppose f(x) is a function satisfying the folowing conditions: (i)f(0)=2,f(1)=1 (ii) f(x) has a minimum value at x=(5)/(2) (iii) for all x f'(x)= |{:(2ax,2ax-1,2ax+b+1),(b,b+1,-1),(2(ax+b),2ax+2b+1,2ax+b):}| The value of f(2)+f(3) is

The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),(3x+2,2lexle4),(2ax+5b,4 < xle8):} If f(s) is continuous on [0,8], find the values of 'a' and 'b'.