Question

HELP! (Urgent pre-calculus question.)

Answer 1

2. means that for every x, there is eactly one y
basically, we can use the vertical line test to see if it crosses at any 2 points

first one works
2nd one works
3rd works
4th works
5th works
they are all one to one functions



3.
easy
steps
for f(x)=?
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)
so


`f(x)=(1+x)^3-2`
replace

`y=(1+x)^3-2`
switch

`x=(1+y)^3-2`
solve

`x+2=(1+y)^3`

`\sqrt[3]{x+2}=1+y`

`-1+\sqrt[3]{x+2}=`
replace

`f^(-1)(x)=-1+\sqrt[3]{x+2}`
first option



4.
domain, hmm we can't divide by 0 so domain is all real numbers except for x=0
domain is
`(-\infty,0) \cup(0,\infty)`
hmm, range
as x approaches negative or positive infinity, f(x)=5
as x approaches 0 from the left, f(x) appraoches negative infintiy
as x approaches 0 from the right , f(x) appraoches positive infintiy
so range is
`(-\infty,5) \cup(5,\infty)`

domain is
`(-\infty,0) \cup(0,\infty)`
range is
`(-\infty,5) \cup(5,\infty)`
answer is the 4th option