Question

For the function f(x)=(7-8x)^2 find f^-1. Determine whether f^-1 is a function.

Answer 1

The inverse of

f(x) = (7-8x)^2

is ............. f-1(x) = 1/8 *(7 ±sqrt(x))

If we plot this graph We can easily see it is not a function

(Fails the vertical line test)

Answer 2

Answer: The inverse of f(x) is not a function because it does not satisfies the vertical line test.

Step-by-step explanation:

The given function is,

`f(x)=(7-8x)^2`

`y=(7-8x)^2`

Interchange the variables and find the value of y to determine the inverse of f(x).

`x=(7-8y)^2`

`\pm √(x)=7-8y`

`y=(7\pm √(x))/(8)`

put
`y=f^(-1)(x)`

`f^(-1)(x)=(7\pm √(x))/(8)`

For each value of x there are two values, so it will not satisfy the vertical line test.

According to vertical line test the graph of a function intersect the vertical line at most once. It means for each x there exist a unique value of y.

Since the
`y=f^(-1)(x)`, does not satisfy the vertical lines test, therefore the inverse of given function is not a function.