Which of the following is/are true?

  • #1
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Homework Statement


Which of the following statements are true?
A)
If f(x)=ex, then f(x)⋅f(-x)=1

B)
If g(x)=1/x, then g (1/x)=x

C)
If h(x)=√(x+2), then h(2)=±2

Homework Equations




The Attempt at a Solution


Only B
 

Answers and Replies

  • #2
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Homework Statement


Which of the following statements are true?
A)
If f(x)=ex, then f(x)⋅f(-x)=1

B)
If g(x)=1/x, then g (1/x)=x

C)
If h(x)=√(x+2), then h(2)=±2

Homework Equations




The Attempt at a Solution


Only B
I agree, but why do you think that A and C are not true?
 
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  • #3
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A) doesn't seem to make sense to me... although x is still unknown.
C)The answer would be 2 not ±2.
 
  • #4
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A) doesn't seem to make sense to me... although x is still unknown.
But even without having a specific value for x, can't you evaluate f(x) - f(-x), to see whether it comes out to 1? Otherwise your answer is nothing more than a guess.
Jaco Viljoen said:
C)The answer would be 2 not ±2.
Yes.
 
  • #5
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9
If f(x)=ex, then f(x)⋅f(-x)=1 Not true:
-ex
 
  • #6
Ray Vickson
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Homework Statement


Which of the following statements are true?
A)
If f(x)=ex, then f(x)⋅f(-x)=1

B)
If g(x)=1/x, then g (1/x)=x

C)
If h(x)=√(x+2), then h(2)=±2

Homework Equations




The Attempt at a Solution


Only B
In (A), it looks to me as though you are writing (i): ##f(x) \times f(-x)##, while Mark44 seems to see (ii): ##f(x) - f(-x)##. Which do you mean: (i) or (ii)?
 
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  • #7
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Oops! My mistake! Thanks for pointing out my error, Ray. I misread that dot as a minus sign. f(x) X f(-x) is indeed equal to 1.
 
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