Which statements about exponential, reciprocal and square root functions are true?

[Jaco Viljoen]

Homework Statement

Which of the following statements are true?
A)
If f(x)=e^x, 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

 

[Mark44]

Homework Statement

Which of the following statements are true?
A)
If f(x)=e^x, 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?

 

[Jaco Viljoen]

A) doesn't seem to make sense to me... although x is still unknown.
C)The answer would be 2 not ±2.

 

[Mark44]

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.

C)The answer would be 2 not ±2.

Yes.

 

[Jaco Viljoen]

If f(x)=e^x, then f(x)⋅f(-x)=1 Not true:
-e^x

 

[Ray Vickson]

Homework Statement

Which of the following statements are true?
A)
If f(x)=e^x, 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)?

 

[Mark44]

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.