Question

If f(x)= sqrt(2-x and g(x) = x − 1, then find the domain of h(x) = f(x)/g(x).

1) (- infinity , 1) U (-1, 2]
2) (- infinity , 1) U (1, 2]
3) (- infinity , 2) U (1, 2]
4) (- infinity , -1) U (1, 2]
5) (- infinity , -2) U (1, 2]

Answer 1

what is the domain of f(x)?

Answer 2

This you want the inside of the square root to be positive or zero

Answer 3

positive means greater than 0

Answer 4

So you have an inequality to solve
2-x>=0

Answer 5

after you solve that we also are going to consider the domain of 1/(x-1)
since g(x) is going to end up on bottom

Answer 6

sorry, I forgot to put the - behind the infinty

Answer 7

@freckles

Answer 8

@MelodicSymphony

Answer 9

it would be the second option because there is an asymptope at x=1 so you would put a parentheses and then it touches the 2 meaning a bracket
i graphed it to better visualize it

Answer 10

simply type the equation here https://www.desmos.com/calculator
to see the graph

Answer 11

Thank you!