Hello people

, I was recently studying relations and functions and encountered some questions that i wasn't able to solve. Please help me solve the following questions.

**1)** Find the range of the functions:

(a) f(x) = 4(x^2) - 4x + 3, x E R

(b) f(x) + 4(x^2) - 4x + 8, x E R

**2)** If f(x) = (x + 3 / x - 5) and y= 3 + 5x / 4x -1 , show that f(y) = x

**3)** If f(x) = (x - 1 / x + 1); x is not equal to -1, show that f( x -1 / x + 1) = -1 / x

**4)** If f(x) = x^2 + 3x -2, -1 ≤ x ≤ 1, find the value of x for which f(x) = f(2x + 1)

**5)** If f(x) = x / 2 and g(x) = 2x + 1, show that 2g [f(x)] = 2f[g(x)] + 1