Question

What is the inverse of the function f(x)=x/5-2

Answer 1

`\huge\boxed{\sf f^(-1)(x)=5x+10}`

Explanation:

Given function:

`\displaystyle f(x)=(x)/(5) -2`

Put f(x) = y

`\displaystyle y=(x)/(5) -2`

Swap x and y

`\displaystyle x = (y)/(5) -2`

Now, solve for y

`\displaystyle x = (y)/(5) -2`

Add 2 to both sides

`\displaystyle x + 2 =(y)/(5)`

Multiply 5 to both sides

`5(x+2)=y`

Distribute

`5x + 10 =y`

Put y = f⁻¹(x)

`\boxed{f^(-1)(x)=5x+10}`

`\rule[225]{225}{2}`