find a for which `ax^(2) + x -1lt 0,AA x in R ?`

find a for which 3x^(2) + ax+3 gt 0,AA x in R.

The value of 'a' for which the equation x^(3) + ax + 1 = 0 and x^(4) + ax^(2) + 1 =0 has a common root is :

Let f, g : R rarrR be two functions defined as f(x) = |x| + x and g(x) = | x| - x AA x in R. . Then (fog ) (x) for x lt 0 is

f : R to R be defined as f(x) = 4x + 5 AA x in R show that f is invertible and find f^(-1) .

Prove that the function f : R to R defined by f(x) = 2x , AA x in R is bijective.

If f(x) = {((1-cos 4x)/x^(2), x lt 0),(a, x =0),((sqrtx)/(sqrt(16+sqrt(x))-4), xgt 0):} then the value of a for which f(x) is continuous at x = 0 is

Let f : R to R be a function defined by f(x) = 4x - 3 AA x in R . Then Write f^(-1) .

Prove that the function f : R to R defined by f(x) = 3 - 4x , AA x in R is bijective.

Draw the graph of the modulus function f: R to R defined by f(x) = |x| AA x in R .