Hi, can someone please help me answer these 7 questions please? More points to t

Question

Hi, can someone please help me answer these 7 questions please? More points to those who provide some sort of explanation. Thank you!

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7)

If the answer is infinity, input infinity; if the answer is -infinity, input -infinity. Given that f(x) = x2 - 4 and g(x) = X - 1, calculate (f g)(x)= , its domain is (g f)(x) = , its domain is (f f)(x) = , its domain is (g g)(x) = , its domain is If a ball is thrown straight up into the air with an initial velocity of 75 ft/s, it height in feet after t second is given by y = 75t - 16t2. Find the average velocity for the time period begining when t = 2 and lasting 0.1 seconds 0.01 seconds 0.001 seconds The graph of the function f(x) = 4x-4 can be obtained from the graph of g(x) = 4x by one of the following actions: shifting the graph of g(x) to the right 4 units; shifting the graph of g(x) to the left 4 units; shifting the graph of g(x) upward 4 units; shifting the graph of g(x) downward 4 units; reflecting the graph of g(x) in the x-axis; reflecting the graph of g(x) in the y-axis; Your answer is (input a, b, c, d, e, or f) Is the domain of the function f(x) still (-infinity, infinity)? Your answer is (input Yes or No) The range of the function f(x) is (A, infinity), the value of A is Find the exponential function f(x) = Cax whose graph goes through the points (0, 4) and (2, 16). a = ,C = . The functions f(x) and g(x) are given in the graph. Find the corresponding function values. If there is no function value, type DNE in the answer blank. (f + g)(1) = (f - g)(2) = Given that f(x) = /x -10 and g(x) = 10/ x + 13, find (f + g) (x) = and its domain is (f - g) (x)= and its domain is (fg) (x) = and its domain is (f/g) (x) = and its domain is Let f(x) = Sketch the graph of this function and find following limits if they exist (if not, enter DNE). f(x) f(x) f(x) f(x) f(x) f(x)

Explanation / Answer

1.)

f(x) = x2 - 4, g(x) = x-1

f(g(x)) = (x-1)2 - 4 = x2 + 1 -2x - 4 = x2 -2x - 3   domain = (-infinity,infinity)

g(f(x)) = x2 - 4 -1 = x2 - 5   domain = (-infinity,infinity)

g(g(x)) = x-1-1 = x-2 domain = (-infinity,infinity)

f(f(x)) = (x2 - 4)2 - 4 = x4 + 16 -8x2 - 4 = x4 -8x2 - 12    domain = (-infinity,infinity)

2.)

y(t) = 75t - 16t2

y(2) = 75(2) - 16*22 = 86

a.) [ y(2.1) - y(2) ] / 0.1 = [86.94 - 86] / 0.1 = 9.4 m/s

b.) [ y(2.01) - y(2) ] / 0.01 = [86.1084 - 86] / 0.01 = 10.84 m/s

c.) [ y(2.001) - y(2) ] / 0.001 = [86.010984 - 86] / 0.001 = 10.984 m/s

3.)

The right option is (a) shifting g(x) to right by 4 units

Yes, the domain is still (-infinity , infinity)

Value of A = 0 in the range

4.)

y = Cax

4 = Ca0

C = 4

16 = 4a2

a = 2

5.)

(f+g)(1) = 1-1 = 0

(f-g)(2) = -2-(-5) = -7

6.)

f(x) = 3/(x-10) , g(x) = 10/ (x+13)

(f+g)(x) = 3/(x-10) + 10/ (x+13) = [ 3(x+13) + 10(x-10) ] / [(x+13)(x-10)] = [ 13x - 61) ] / [(x+13)(x-10)]

Domain = (-infinity,infinity) {-13 , 10}

(f-g)(x) = 3/(x-10) - 10/ (x+13) = [ 3(x+13) - 10(x-10) ] / [(x+13)(x-10)] = [ -7x + 139) ] / [(x+13)(x-10)]

Domain = (-infinity,infinity) {-13 , 10}

(f.g)(x) = [ 3/(x-10) ]*[ 10/ (x+13) ] =30 / [(x+13)(x-10)]

Domain = (-infinity,infinity) {-13 , 10}

(f/g)(x) = [ 3/(x-10) ] / [ 10/ (x+13) ] = [ 3(x+13) / 10(x-10) ]

Since the numerator f(x) and g(x) both need to exist under x lying in the domain. Hence the domain remains the same

Domain = (-infinity,infinity) {-13 , 10}

7.)

1.) 3

2.) 9

3.) DNE

4.) 11

5.) 9-(-2) = 11

6.) 11

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