Find the equation of the inverse of f(x) =1/2x+4.

Question

F(x) 1/2X+4

1) Graph the function and its inverse on one coordinate plane

2) Show the line of symmetry of the graph.

Answer 1

(1)

The Function is F(x) = (1/2)x+4

Let us assume f(x) = y and solve x in terms of y.

y = (1/2)x + 4

Subtract 4 from each side.

y - 4 = (1/2)x

Multiply by 2 on each side.

2(y - 4) = x

Now interchange x and y.

2(x - 4) = y

Replace y by  .

The inverse of the function is 2(x-4).

Graph

Therefore the inverse of the function F(x) = (1/2)x+4 is .

Answer 2

(2)

Let us find the composite function

Similarly

We can observe that  both of the composite functions are equal which means they are symmetry to each other.

The line of Symmetry is y = x

Graph

Therefore the line of Symmetry is y = x.