Question

Find the formula for f⁻¹(x) for the function f(x)=(2x+1)/(3x)

Answer 1

To find the formula for f⁻¹(x) for the function f(x)=(2x+1)/(3x), follow these steps: rewrite the equation, cross-multiply, isolate the term, and divide by 2.

Step-by-step explanation:

To find the formula for f⁻¹(x) for the function f(x)=(2x+1)/(3x), we need to solve for x in terms of f(x). Let's start by rewriting the equation with f(x) in place of x:

(2f⁻¹(x) + 1)/(3f⁻¹(x)) = x

Now, we can cross-multiply to eliminate the fractions:

2f⁻¹(x) + 1 = 3xf⁻¹(x)

Next, we can solve for f⁻¹(x) by isolating the term:

2f⁻¹(x) = 3xf⁻¹(x) - 1

Finally, divide both sides by 2 to solve for f⁻¹(x):

f⁻¹(x) = (3xf⁻¹(x) - 1)/2