To Find: Determine the following values a) (f+g)(2) b) (f-g)

slaggingV 2021-09-20 Answered
To Find: Determine the following values
a) (f+g)(2)
b) (fg)(12)
c) (fg)(4)
d) (fg)(0)
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Expert Answer

Caren
Answered 2021-09-21 Author has 96 answers
Given: The functions f(x)=2x+1 and g(x)=1x
We can define addition of two functions as follows
(f+g)(x)=f(x)+g(x)
We can define subtraction of two functions as follows
(fg)(x)=f(x)g(x)
We can define multiplication of two functions as follows
(fg)(x)=f(x)×g(x)
We can define division of two functions as follows
(fg)(x)=f(x)g(x)
Calculation:
a) Since (f+g)(x)=f(x)+g(x)
Substituting f(x) and g(x) we get,
(f+g)(x)=2x+1+1x
Substituting x=2 we get,
(f+g)(2)=2(2)+1+12
(f+g)(2)=5+12
(f+g)(2)=112
b) Since (fg)(x)=f(x)g(x)
Substituting f(x) and g(x) we get,
(fg)(x)=2x+11x
Substituting x=12 we get,
(fg)(12)=2(12)+1112
(fg)(12)=1+12
(fg)(12)=0
c) Since (fg)(x)=f(x)g(x)
Substituting f(x) and g(x) we get,
(fg)(x)=(2x+1)(1x)
Substituting x=4 we get,
(fg)(4)=(2×4+1)(14)
(fg)(4)=(94)
d) Since (fg)(x)=f(x)g(x)
Substituting f(X) and g(x) we get,
(fg)(x)=(2x+1)(1x)
(fg)
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