Question

continuous functions
https://i.gyazo.com/9ff0525007699edda3be45abf99ce930.png
How do you do (e)?? It says f(x)g(x) what am I supposed to do there? How do i multiply both of those functions?

Answer 1

f(x)g(x) = g(x) when x <> 4
f(x)g(x) = -g(x) when x = 4

Answer 2

TK :') <3

Answer 3

wait what? which expression in g(x)?

Answer 4

why would it equal g(x)?

Answer 5

The one indicated in the expressions.

f(x)g(x) = 4x-10 when x<>4
f(x)g(x) = 6 when x=4

Answer 6

but it's asking if it's continuous

Answer 7

wait so how does this work? you multiply the functions side by side?

Answer 8

@tkhunny

Answer 9

also why isn't (c) continuous?

Answer 10

does anyone know?

Answer 11

i think you multiply each interval,

f*g then 4x - 10 and +6, notice at x=4 now the value is +6, and the 4x-10 has a limit of +6 at x=4

Answer 12

it used to be a removed point discontinuity for x=4,
the product , moves that point back up to +6 and completes the curve, smooth

Answer 13

yeah the limit as x goes to 4 of g(x) is +6, the value of 4x - 10 goes to +6 moving closer and closer from both left and right sides

Answer 14

the only thing missing for continuity of g(x)is the single point value when x=4 , it is at -6 instead

Answer 15

the product with f(x) changes that value of x=4 to +6 , and now it is a continuous curve

Answer 16

For c), if g(x) isn't continuous, do you think -g(x) will be continuous?

Multiplying a function by a constant can not change the functions continuity. Neither can adding or subtracting a constant from the function.

Answer 17

yes, that makes sense