Question

Find the inverse of the function f(x)=24+4x​

Answer 1

Answer: the inverse of the function f(x) = 24 + 4x is f^-1(x) = (x - 24) / 4.

Step-by-step explanation: To find the inverse of the function f(x) = 24 + 4x, we can follow these steps:

Step 1: Replace f(x) with y.

y = 24 + 4x

Step 2: Swap the positions of x and y.

x = 24 + 4y

Step 3: Solve for y in terms of x.

x = 24 + 4y

x - 24 = 4y

y = (x - 24) / 4

Step 4: Replace y with f^-1(x).

f^-1(x) = (x - 24) / 4

Answer 2

`\huge\boxed{\sf \displaystyle f^(-1)(x)=(x-24)/(4) }`

Explanation:

Given function:

f(x) = 24 + 4x

• Put f(x) = y

y = 24 + 4x

• Exchange y and x

x = 24 + 4y

• Solve for y

x = 24 + 4y

• Subtract 24 from both sides

x - 24 = 4y

• Divide 4 to both sides

`\displaystyle (x-24)/(4) = y`

• Put y = f⁻¹(x)

`\boxed{\displaystyle f^(-1)(x)=(x-24)/(4) }\\\\\rule[225]{225}{2}`