Question

Given that f(x) = 4x+1/3, solve for f^-1(3)

Answer 1

The value is 2/3

Explanation:

In order to find this, we first need to find the inverse of the equation (f^-1). To do this, switch f(x) and x and then solve for the new f(x).

f(x) = 4x + 1/3

x = 4f(x) + 1/3

x - 1/3 = 4f(x)

1/4x - 1/12 = f(x)

f^-1(x) = 1/4x - 1/12

Now that we have the inverse function, we simply need to plug in 3 for x and we get the value we are searching for.

f^-1(x) = 1/4(3) - 1/12

f^-1(x) = 3/4 - 1/12

f^-1(x) = 9/12 - 1/12

f^-1(x) = 8/12

f^-1(x) = 2/3

Answer 2

The solution for the function, f⁻¹(3) is 2/3

To solve for f⁻¹(3), we need to find the value of x for which f(x) = 3. Here's how we can do it:

Set f(x) equal to 3:

4x + 1/3 = 3

Subtract 1/3 from both sides to isolate x:

4x = 8/3

Divide both sides by 4 to find x:

x = 2/3

Therefore, f⁻¹(3) = 2/3. This means that when the input to f(x) is 3, the output is 2/3.