Question

let the function f be defined by f(x)=2x+1/1-3x then f^-1(x) is​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{f(x) = \frac{2x + 1}{1 - 3x} }$

TO DETERMINE

$\displaystyle \sf{ {f}^{ - 1}(x) }$

EVALUATION

Let

$\displaystyle \sf{y = {f}^{ - 1}(x) }$

$\displaystyle \sf{ \implies \: x = f(y)}$

$\displaystyle \sf{ \implies \: x = \frac{2y + 1}{1 - 3y} }$

$\displaystyle \sf{ \implies \: x - 3xy = 2y + 1}$

$\displaystyle \sf{ \implies \: x -1 = 3xy + 2y }$

$\displaystyle \sf{ \implies \: x -1 = y(3x + 2) }$

$\displaystyle \sf{ \implies \: y = \frac{x - 1}{3x + 2} }$

$\displaystyle \sf{ \implies \: {f}^{ - 1} (x) = \frac{x - 1}{3x + 2} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Evaluate f(x) = x4 - 7x2 + 2x - 6 at x = 1

https://brainly.in/question/32494746

2..The polynomial f(x) = x⁴ - 2x³ - px² + q is divisible by (x-2)². Find the values p and q. Hence, solve the equation.

https://brainly.in/question/27895807

Answer 2

Answer:

Answer attached in the image above.

Hope this helps you!