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pantera1 [17]
4 years ago
13

If f(x) = x+7 and g(x) = 1/x-13 , what is the domain of (f•g)(x)?

Mathematics
2 answers:
dimulka [17.4K]4 years ago
7 0

Answer:

The domain of the given equation is D=[x|x\neq 13]                              

Step-by-step explanation:

Given : If f(x)=x+7 and g(x)=\frac{1}{x-13}

To find : What is the domain of (fog)(x)?

Solution :

We can write,

(fog)(x)=f(g(x))

(fog)(x)=f(\frac{1}{x-13})

(fog)(x)=\frac{1}{x-13}+7

(fog)(x)=\frac{1+7x-91}{x-13}

(fog)(x)=\frac{7x-90}{x-13}

We have seen that (fog)(x) to be defined when denominator cannot be zero.

i.e.   x-13\neq0

 x\neq13

So, The domain of the given equation is D=[x|x\neq 13]

MArishka [77]4 years ago
6 0
(f*g)(x)= (x+7)(1/x-13)

= (x+7)/(x-13)

so the domain ( -∞, 13)U(13,∞)
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