Question

Write the set of x-values where the function is continuous using interval notation
f(x)=|9x-7|+5sin(8x)

Answer 1

This function has two main parts. It's clear. Do you recognize them?

Answer 2

I do not

Answer 3

If you want to divide it to two parts, how will you do that?

Answer 4

let me see here, would it be |9x+7| and 5sin(8x) ?

Answer 5

correct
Now! what do you think about the Sine function? Is it continuous for all Xs?

Answer 6

Yes I believe so

Answer 7

it's correct.
What do you think about the absolute value part?

Answer 8

I think this is also continous

Answer 9

Let me ask you one thing: Are you sure the question is not asking if it's DIFFERENTIABLE in definite ranges of X ?

Answer 10

I am sure :)

Answer 11

so! :) The sum of two continuous functions IS another continuous function.
Minus Infinity to plus infinity

Answer 12

so the x values would be [-infinity,inifnity] ?

Answer 13

yes! Until you add two continuous functions, it results in another continuous function.

Answer 14

But actually i think it's kind of weird. I suggest you double-check the function.

Answer 15

By the way, for infinity you must use a proper sign. Brackets is not proper.

Answer 16

thank you for your help :)

Answer 17

use parenthesis instead of brackets.