Compute

[nycmath]

See attachment.

[Eigenvalue]

g(x)=1-2x
Domain: all real numbers; all linear equations have a domain of all real numbers
Range: all real numbers; all linear equations have a range of all real numbers
x-intercept (0.5,0)
y-intercept (0,1)

[tex]g^{-1 }[/tex](x): x=1-2y
2y=1-x
y=[tex]\frac{1-x}{2}[/tex]

(g(x))'=(1-2x)'=-2

[tex]\frac{g(x+h)-g(x)}{h}[/tex]

=[tex]\frac{1-2(x+h)-(1-2x)}{h}[/tex]

=[tex]\frac{-2h}{h}[/tex]
=-2

[nycmath]

g(x)=1-2x
Domain: all real numbers; all linear equations have a domain of all real numbers
Range: all real numbers; all linear equations have a range of all real numbers
x-intercept (0.5,0)
y-intercept (0,1)

[tex]g^{-1 }[/tex](x): x=1-2y
2y=1-x
y=[tex]\frac{1-x}{2}[/tex]

(g(x))'=(1-2x)'=-2

[tex]\frac{g(x+h)-g(x)}{h}[/tex]

=[tex]\frac{1-2(x+h)-(1-2x)}{h}[/tex]

=[tex]\frac{-2h}{h}[/tex]
=-2

You did not explain why the domain and range equal all real numbers for linear functions. This leaves the student bewildered.