Composite Functions

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

For the given functions f and g, find (f + g)(x) and
(f - g)(x). Also, find the domain.

See attachment.

[Eigenvalue]

75. (f-g)(x)=[tex]\frac{2x+3-4x}{3x-2}[/tex]=[tex]\frac{-2x+3}{3x-2}[/tex]
(f+g)(x)=[tex]\frac{2x+3+4x}{3x-2}[/tex]=[tex]\frac{6x+3}{3x-2}[/tex]

74. (f-g)(x)=[tex]\sqrt{x-1}[/tex]-[tex]\sqrt{4-x}[/tex]
(f+g)(x)=[tex]\sqrt{x-1}[/tex]+[tex]\sqrt{4-x}[/tex]

[nycmath]

75. (f-g)(x)=[tex]\frac{2x+3-4x}{3x-2}[/tex]=[tex]\frac{-2x+3}{3x-2}[/tex]
(f+g)(x)=[tex]\frac{2x+3+4x}{3x-2}[/tex]=[tex]\frac{6x+3}{3x-2}[/tex]

74. (f-g)(x)=[tex]\sqrt{x-1}[/tex]-[tex]\sqrt{4-x}[/tex]
(f+g)(x)=[tex]\sqrt{x-1}[/tex]+[tex]\sqrt{4-x}[/tex]

Excellent work.