Consider the function of f(x)=2/7-x. a. What is f(7)?b. What is the domain of f(x)?c. If g(x)=2x+5, what is g(3)?d. Now use the output of g(3) as the input for f to calculate f(g(3))?

Answer 1

a. f(7) = 2/7 - 7 ---- plug in "7" for "x"

= (2/7) - (49/7)

= -47/7

b. All real numbers because there are two rules: 1) can't divide by 0. 2) can't take the square root of a negative number. This equation doesn't involve either so it's all real numbers.

c. g(3) = (2*3) + 5 ----- plug in "3" for "x"

= 6 + 5

= 11

d. f(g(3)) = f(11) ---- plug in "11" for "x"

f(11) = 2/7 - 11

= (2/7) - (77/7)

= -75/7

IF YOU MEANT 2/(7-x)

a. f(7) = 2/(7-7)

= 2/0 <-- UNDEFINED

b. *can't divide by 0 so take the denominator and set it equal to 0

7 - x = 0

x = 7

THEREFORE domain is All Real Numbers except when x = 7.

c. g(3) = (2*3) + 5 ----- plug in "3" for "x"

= 6 + 5

= 11

d. f(g(3)) = f(11) ---- plug in "11" for "x"

f(11) = 2/(7-11)

= 2/(-4)

= -1/2

Answer 2

f(x) = 2/(x-7)

f(7) = 2/0 which is undefined, UNLESS you really meant f(x) =(2/x)-7 then f(7) =2/7 - 7 = - 47/7= 6 5/7. Domain is all real numbers except 7 for the f(x)=2/(x-7) but all real number if f(x) = (2/x)-7

g(x) = 2x+5, g(3) = 2(3)+5 = 6+5= 11

f(g(3)) = 2/(x-7) = 2/(11-7) = 2/4 = 1/2

UNLESS you meant f(x) = (2/x)-7, then f(g(3)) = (2/11)-7 = -73/11 = -6 7/11

Answer 3

f(x) = 2/(7-x)

a) What is f(7)? Just plug in x=7"

f(7) = 2/(7-7) = 2/0

b) Now division by zero is undefined, so f(7) is undefined and x = 7 is excluded from the domain of f(x). So the domain is all real numbers except x = 7

c) To find g(3), just plug x = 3 into g(x)

d) To find f(g(3)), just set x = g(3) from part (c) and plug into f(x).