What is the answer to f(x)=-2(x-1)(x+4)

y

=

2

x

−

8

is the inverse of

y

=

1

2

x

+

4

and it is a linear function.

Explanation:

From the given

y

=

1

2

x

+

4

interchange the variables first

x

=

1

2

y

+

4

solve for y in terms of x

y

=

2

x

−

8

let us check using the graphs compared to

y

=

x

graph{(y-1/2x-4)(y-2x+8)(y-x)=0[-20,20,-10,10]}

Notice that the line

y

=

x

acts as the mirror line. Therefore the equations above are inverses of each other.

I hope the explanation is useful.

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