Question

If f(x)=sqrt2-x and g(x) = x − 1, then find the domain of h(x) = f(x) g(x).

Answer 1

you wrote `h(x) = f(x) g(x)` but there's a gap between f(x) and g(x). Is there a symbol missing?

Answer 2

division symbol

Answer 3

is f(x) this?

\[\Large f(x) = \sqrt{2-x}\]

OR is it this?

\[\Large f(x) = \sqrt{2}-x\]

Answer 4

the first

Answer 5

so h(x) would be

\[\Large h(x) = \frac{f(x)}{g(x)}\]
\[\Large h(x) = \frac{\sqrt{2-x}}{x-1}\]

Answer 6

Question: which value of x makes the denominator, x-1, equal to 0?

Answer 7

so confused

Answer 8

if x-1 = 0, then what must x be?

Answer 9

1

Answer 10

since x = 1 makes x-1 = 0 true, that means x = 1 makes the denominator equal to zero. Agreed?

Answer 11

yes

Answer 12

to avoid dividing by zero, we have to kick out x = 1 from the domain

Answer 13

now onto the next part

Answer 14

when you solve \(\Large 2 - x \ge 0\) for x, what do you get?

Answer 15

i dont even know how to solve that, ive had sucky math teachers in high school they passed you based on if they liked you

Answer 16

why not add x to both sides?