Question

Find the inverse of the function. Is the inverse a function?

y = 8x-2
y = (Simplify your answer.)

Answer 1

Hi, there.

_____

Here's how we can find the inverse of a function:

1. Swap x's and y's.
2. Solve in terms of y.

(1)

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

(2)

Divide both sides by 8. Be sure to divide each and every term by 8.

`\boldsymbol{(x)/(8)=y-(2)/(8)}`

Next, subtract both sides by x/8. Subtract bothsides by y also.

`\boldsymbol{-y=-(x)/(8)-(2)/(8)}`

To finish this off divide each and every term by -1.

`\boldsymbol{y=(x)/(8)+(2)/(8)}`

We can also reduce the fraction 2/8.

`\boldsymbol{y=(x)/(8)+(1)/(4)}`

We can also write

f⁽⁻¹⁾

instead of y.

`\boldsymbol{f^((-1))=(x)/(8)+(1)/(4)}`

Hope the answer - and explanation - made sense,

happy studying.

Answer 2

Answer:
`f^(-1)(x) = (x)/(8) + (1)/(4)`

yes this is a function

Explanation:

To find if something is an inverse, switch x and y. Then solve for y.

`y = 8x - 2`

`x=8y-2`

`x+2=8y`

`y=(x+2)/(8)`

`y=(x)/(8) + (1)/(4)`

`\large\boxed{f^(-1)(x) = (x)/(8) + (1)/(4)}`

yes this is a function