Answer:
Step-by-step 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 = [tex]-\frac{x}{0.5}[/tex]
y = -2x
Inverse function will be,
[tex]g^{-1}x=-2x[/tex]
2). h(x) = 4x
Equation form of the function will be,
y = 4x
Interchange x and y,
x = 4y
Solve for y,
y = [tex]\frac{x}{4}[/tex]
Inverse function will be,
[tex]h^{-1}(x)=0.25x[/tex]
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) = [tex]\frac{x}{2}[/tex]
Equation form of the function will be,
y = [tex]\frac{x}{2}[/tex]= x
Interchange x and y,
x = [tex]\frac{y}{2}[/tex]
Solve for y,
y = 2x
Therefore, inverse function will be,
[tex]f^{-1}(x)=2x[/tex]
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,
[tex]k^{-1}(x) =x[/tex]
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,
[tex]p^{-1}(x)=x - 4[/tex]
