Question

If f(x)=(1)/(4)x+3, what is the equation for f-¹(x)?

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf f(x) = (1)/(4x + 3)$}`

`\Large \text{$ \sf y = (1)/(4x + 3)$}`

`\Large \text{$ \sf x = (1)/(4y + 3)$}`

`\Large \text{$ \sf x\:[\:4y + 3\:] = 1$}`

`\Large \text{$ \sf 4y + 3 = (1)/(x)$}`

`\Large \text{$ \sf 4y = (1)/(x) - 3$}`

`\Large \text{$ \sf 4y = (1 - 3x)/(x)$}`

`\Large \text{$ \sf y = (1 - 3x)/(4x)$}`

`\Large \boxed{\boxed{\text{$ \sf f^(-1)(x) = (1 - 3x)/(4x)$}}}`

Answer 2

To find the inverse function f⁻¹(x) of f(x)=(1/4)x+3, swap x and y in the equation and then solve for y. The equation for the inverse of f(x) = (1/4)x + 3 is f-1(x) = 4x - 12.

Step-by-step explanation:

The equation for the inverse of a function f(x) can be obtained by swapping the x and y variables in the original function and solving for y. In this case, the original function is f(x) = (1/4)x + 3. To find the inverse, we replace f(x) with y and x with f-1(x). So, the equation becomes x = (1/4)y + 3. We can then solve for y by isolating it on one side of the equation:

f-1(x) = 4x - 12

To find the inverse function, f-1(x), of the given function f(x)=(1/4)x+3, perform the following steps:

1. Replace f(x) with y: y = (1/4)x + 3.
2. Switch x and y: x = (1/4)y + 3.
3. Solve for y: y = 4(x - 3).

Therefore, the equation for the inverse function is f-1(x) = 4(x - 3).