Question

Pls help; use inverse operations to write the inverse of F(x)= x/4 - 5

Answer 1

`\huge \boxed{F^(-1)(x)=4(x+5)}`

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

Explanation:

`\displaystyle F(x)= (x)/(4) - 5`

`\displaystyle y= (x)/(4) - 5`

Switching variables,

`\displaystyle x= (y)/(4) - 5`

Solving for y,

`\displaystyle x+5= (y)/(4)`

`4(x+5)=y`

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

Answer 2

`f^(-1)(x)=4(x+5)`

Explanation:

So we have the function:

`f(x)=(x)/(4)-5`

To find the inverse of a function, switch f(x) and x, change f(x) to f⁻¹(x), and solve for it. Thus:

`x=(f^(-1)(x))/(4)-5`

Add 5 to both sides:

`x+5=(f^(-1)(x))/(4)`

Multiply both sides by 4:

`f^(-1)(x)=4(x+5)`

And we're done!

Hope this helps!