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If f(x) = 4x + 5, which of these is the inverse of f(x)?​

If f(x) = 4x + 5, which of these is the inverse of f(x)?​-example-1

2 Answers

3 votes

Final answer:

To find the inverse of the function f(x) = 4x + 5, switch x and y in the equation, then solve for y to get the inverse function, which is f-1(x) = (x - 5) / 4.

Step-by-step explanation:

To find the inverse of the function f(x) = 4x + 5, you would follow these steps:

  1. Replace f(x) with y: y = 4x + 5.
  2. Switch the roles of x and y: x = 4y + 5.
  3. Solve the equation for y to find the inverse function:
  • Subtract 5 from both sides: x - 5 = 4y.
  • Divide by 4: y = (x - 5) / 4.
The inverse function is: f-1(x) = (x - 5) / 4.

This inverse function will satisfy the condition that f(f-1(x)) = x and f-1(f(x)) = x, which is the defining property of an inverse function.

User Oillio
by
7.9k points
2 votes

Answer:

A

Step-by-step explanation:

y=4x+5

x=4y+5

4y+5=x

4y+5-5=x-5

4y=x-5

4y/4= x/4 - 5/4

y= x-5/4

User Aqeel Ahmad
by
7.7k points

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