Question
Asked Oct 8, 2019
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f(x)=1/x-7 and g(x)=1/x-1 then the domain of f o g is equal to all reals except for two values , a and  b with a less than b 

a=

b= 

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Expert Answer

Step 1

Refer to the question we have to find the domain of (f o g)(x) is equal to all real values except for two values, a and b with a less than b for the provided functions f(x)=1/x-7 and g(x)=1/x-1.

1
1
and g(x)=
f(x) 7
help_outline

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1 1 and g(x)= f(x) 7

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Step 2

Now to the find the composite function (f o g)(x), it is equal to f(g(x)) then put the value of g(x) for the x in the f(x) as,

1
1
f(x)
and g(x)
fog(x) f(g(x))
1
8(x)-7
1
fog (x)
1
- 7
x-1)
help_outline

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1 1 f(x) and g(x) fog(x) f(g(x)) 1 8(x)-7 1 fog (x) 1 - 7 x-1)

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Step 3

Now the domain of the function is defined as that v...

Then, g (x)0
x-10
a 1
1
fog(x)=
1
-7
And also
1
0
1
-7
_
x-1
-7x710
-7x8 0
8
b x
7
a=1b
7
help_outline

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Then, g (x)0 x-10 a 1 1 fog(x)= 1 -7 And also 1 0 1 -7 _ x-1 -7x710 -7x8 0 8 b x 7 a=1b 7

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