NEED asap! let f(x)= 4x-1/2x+3. find a formula for f^-1 (x). (assume that f is one to one)

Question

let f(x) = 4x-1/2x+3. find a formula for f^-1(x). assume f is one to one and express your formula as an equation with f^-1(x) on one side. verify your formula is correct.

Answer 1

F9x) is one-to-one for x > -3/2 then range: (-∞,∞).

y = 4x - 1/(2x + 3); x = 4y - 1/(2y + 3); 2yx + 3x = 8y² + 12y - 1; 8y² + (12 - 2x)y - (3x + 1) = 0

y = (x - 6 ± √x² - 12x + 36 + 24x + 8)/8 = (x - 6 ± √x² + 12x + 44)/8

f^-1(x) = (x- 6 + √x² + 12x + 44)/8 for all real x.