Question

Match each function with the expression representing Its Inverse function.

1. g(x)= -0.5 x
2. h(x)= 4 x
3. y= x - 4
4. f(x)= x/2
5. k(x) = x
6. p(x) = x+4​

Answer 1

Explanation:

1). g(x) = -0.5x

Equation form of the given function is,

y = -0.5x

Interchange x and y,

x = -0.5y

Solve for y,

y =
`-(x)/(0.5)`

y = -2x

Inverse function will be,

`g^(-1)x=-2x`

2). h(x) = 4x

Equation form of the function will be,

y = 4x

Interchange x and y,

x = 4y

Solve for y,

y =
`(x)/(4)`

Inverse function will be,

`h^(-1)(x)=0.25x`

3). y = x - 4

Interchange x and y,

x = y - 4

Solve for y,

y = x + 4

Therefore, inverse of the linear equation is,

y = x + 4

4). f(x) =
`(x)/(2)`

Equation form of the function will be,

y =
`(x)/(2)`= x

Interchange x and y,

x =
`(y)/(2)`

Solve for y,

y = 2x

Therefore, inverse function will be,

`f^(-1)(x)=2x`

5). k(x) = x

Equation form of the function will be,

y = x

Interchange x and y,

x = y

Solve for y,

y = x

Inverse of the function 'f' will be,

`k^(-1)(x) =x`

6). p(x) = x + 4

Equation form of the function will be,

y = x + 4

Interchange x and y,

x = y + 4

Solve for y,

y = x - 4

Inverse of the function 'p' will be,

`p^(-1)(x)=x - 4`