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

User Minyi Han
by
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2 Answers

2 votes

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

User Max Cruz
by
8.3k points
5 votes

Answer:


\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}

User Sedat Kumcu
by
8.2k points

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