Section 2.2 Algebra of Functions

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L e t f (x) = x^{3} + 3 a n d g (x) = x^{2} - 2 . F i n d t h e r u l e o f t h e f u n c t i o n . f - g

L e t f (x) = x^{3} + 7 a n d g (x) = x^{2} - 8 . F i n d t h e r u l e o f t h e f u n c t i o n s g f

L e t f (x) = x^{3} + 5, g (x) = x^{2} - 9, a n d h (x) = 8 x + 7 . F i n d t h e r u l e f o r t h e f u n c t i o n . \frac{f - g}{h}

F i n d t h e f u n c t i o n s f + g, f - g, f g a n d \frac{f}{g} f (x) = \sqrt{x - 6}; g (x) = x^{3} + 6

F i n d t h e r u l e s f o r t h e c o m p o s i t e f u n c t i o n s f \circ g a n d g \circ f f (x) = 2 x^{2} + 9 x + 8; g (x) = x + 3

F i n d t h e r u l e s f o r t h e c o m p o s i t e f u n c t i o n s f \circ g a n d g \circ f f (x) = 7 \sqrt{x} + 1; g (x) = x^{2} + 4

7 .

F i n d t h e r u l e s f o r t h e c o m p o s i t e f u n c t i o n s f \circ g a n d g \circ f f (x) = \sqrt{x + 8}; g (x) = \frac{1}{x - 8}

F i n d f (a + h) - f (a) f o r t h e f u n c t i o n . S i m p l i f y y o u r a n s w e r . f (x) = - \frac{1}{2} x + 7

F i n d f (a + h) - f (a) f o r t h e f u n c t i o n . S i m p l i f y y o u r a n s w e r . f (x) = x^{2} - 3 x + 4

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This question is taken from Math 238 – Calculus for Business and Social Sciences » Summer 2022 » Homeworks