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Given f(x)=1/x+5 and g(x)=x-2

What are the restrictions of f(g(x))
A. x=-5
B. x=-3
C. x=2
D.There are no restrictions

1 Answer

3 votes

For this case we have the following functions:


f (x) = \frac {1} {x + 5}\\g (x) = x-2

We must find f (g (x)). So:


f (g (x)) = \frac {1} {(x-2) +5} = \frac {1} {x-2 + 5} = \frac {1} {x + 3}

Finally we have to:


f (g (x)) = \frac {1} {x + 3}

For the function to be defined the denominator must be different from 0. That is x different from -3.

Answer:

Option B

User Skydv
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