Math 121, Practice Questions Hints And Answers printable pdf download

Math 121, Practice Questions Hints And Answers

Math 121, Practice Questions, October 21

Hints and Answers

1. Let f (x) = 3x + 4x

5. Find and simplify the diﬀerence quotient of f .

Answer: The diﬀerence quotient is

f (x + h)

f (x)

3(x + h) + 4(x + h)

(3x + 4x

3(x + 2xh + h ) + 4x + 4h

4x + 5

3x + 6xh + 3h + 4x + 4h

4x + 5

h(6x + 3h + 4)

= 6x + 3h + 4.

Therefore, the diﬀerence quotient is 6x + 3h + 4

2. Let f (x) = x

11x and g(x) = 2x + 3. Find (a) f

g and (b) g f .

Answer: (a) (f g)(x) = f (g(x)) = (g(x))

11(g(x)) = (2x + 3)

11(2x + 3) = 4x + 12x +

(22x + 33) = 4x

10x

24.

Therefore, (f

g)(x) = 4x

10x

(b) (g f )(x) = g(f (x)) = 2f (x) + 3 = 2(x

11x) + 3 = 2x

22x + 3.

Therefore, (g f )(x) = 2x

22x + 3

3. Find the equation of the line that is parallel to the line 3x + 2y = 7 and passes through the

point ( 2, 4) . Write your answer in slope-intercept form.

Answer: The slope of the parallel line is m =

3/2. Therefore, y + 4 =

(x + 2), which in

slope-intercept form is:

y =

Math 121, Practice Questions Hints And Answers