Answer:
- [tex]f(x)=\sqrt{x+3}[/tex]
- [tex]f(x)=\dfrac{1}{(x-2)(x-4)}[/tex]
Step-by-step explanation:
a) It can be convenient to use the square root function as one being defined only for values greater than or equal to some number. Here, we need to shift that function 3 units to the left, so its domain is [-3, ∞).
[tex]f(x)=\sqrt{x+3}[/tex]
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b) One way to put holes in a function is to put vertical asymptotes there. This function can be defined to have vertical asymptotes at x=2 and x=4 so those values are excluded from the domain.
[tex]f(x)=\dfrac{1}{(x-2)(x-4)}[/tex]
