Question

F(x)=2x+8 find inverse

Answer 1

Answer:To find the inverse of the function f(x) = 2x + 8, we can follow these steps:

1. Start with the given function f(x) = 2x + 8.

2. Replace f(x) with y to represent the inverse function.

3. Swap x and y to interchange the variables. The equation becomes x = 2y + 8.

4. Solve the equation for y. Subtract 8 from both sides: x - 8 = 2y.

5. Divide both sides by 2 to isolate y: (x - 8) / 2 = y.

6. Simplify the equation: y = (x - 8) / 2.

7. Replace y with f^(-1)(x) to represent the inverse function.

8. The inverse function of f(x) = 2x + 8 is f^(-1)(x) = (x - 8) / 2.

The inverse function allows us to find the original input value (x) when given an output value (f(x)). In this case, it enables us to determine the original value of x when given a value of y in the function f^(-1)(x).

Answer 2

Answer:
`\bf{y=\cfrac{x-8}{2}}`

Explanation:

We need to calculate the inverse of the function
`\bf{f(x)=2x+8}`.

To do this, you should follow these steps:

⇒ Replace f(x) with y:
`\bf{y=2x+8}`

⇒ Swap the x's and y's:
`\bf{x=2y+8}`

⇒ Solve for y:

`\bf{x=2y+8}`

`\bf{x-8=2y}`

`\bf{\cfrac{x-8}{2}=y}`

Therefore, the inverse of the function is:
`\boxed{\bf{y=\cfrac{x-8}{2}}}`.

Remember this...

→ An inverse function does the opposite things in the opposite order. The function f(x) = 2x + 8 multiplied x by 2 and then adds 8; its inverse subtracts 8 and then divides by 2.