Question

PLEASE HELP ASAP
Which function has an inverse that is a function

Answer 1

Options (1) and (3)

Explanation:

Option (1)

f(x) = x²+ 3

We can rewrite the function in the equation form as,

y = x² + 3

By interchanging y by x,

x = y² + 3

Now we solve it for y,

y² = x - 3

y = ±√(x - 3)

So the inverse function is,

`f^(-1)(x)=\pm √(x-3)`

It's a function.

Option 2

d(x) = -9

Equation form of the function is,

y = -9

Replacing y by x,

x = - 9

Therefore, inverse function will be,

x = -9

Inverse is not a function

Option 3

m(x) = -7x

Equation form of the function,

y = -7x

Interchanging y by x,

x = -7y

Now solve for x,

y =
`-(1)/(7)x`

So the inverse function will be,

`m^(-1)(x)=-(1)/(7)x`

Inverse is a function.

Option 4

p(x) = |x|

As this function not a one to one function inverse function is not possible.

Inverse of |x| is not a function.