Question

Find the inverse of the function f(x) = 2x² - 3x NO ABSURD ANSWERS IF YOU DON't WANT YOURSELVES TO GET REPORTED!

Answer 1

Answer:

$\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}$

Step-by-step explanation:

$f(x)=2x^2-3x$

$f(x)=y$

$y=2x^2-3x$

Switch variables.

$x=2y^2-3y$

Solve for y.

Multiply both sides by 8.

$8x=16y^2-24y$

Add 9 on both sides.

$8x+9=16y^2-24y+9$

Take the square root on both sides.

$\sqrt{8x+9} =\sqrt{16y^2-24y+9}$

Add 3 on both sides.

$\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3$

Divide both sides by 4.

$\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}$

Simplify.

$\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}$

$\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}$

$\frac{\sqrt{8x+9}+3}{4}=y$

Inverse y = $f^{-1}(x)$

$f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}$