Determine which two functions are inverses of each other? Help?

Question

Here's the problem:

f(x)=5x g(x)=x/5 h(x)=5/x

(A) g(x) and h(x)

(B) f(x) and g(x)

(C) f(x) and h(x)

(D) None

Is it D?

Answer 1

to find the inverse function of a function, swap x and y and rearrange terms.

f(x)=5x

inverse version

y = 5x

x = 5y

y = x/5

so f and g are inverse functions, B.

Disregard previous answer, totally wrong.

More complicated inverse functions:

y = e^x

x = e^y

ln x = y

so e^x and ln x are inverse functions.

Answer 2

The answer is C

To find the inverse function of a function f(x), substitute 1/x for x in the equation.

For f(x) = 5x, substituting gives:

5 * (1/x) = 5/x

which is equal to h(x).

The inverse function of g(x)=x/5 would be:

(1/x) * 5 = 1/(5x)

so g(x) is not the inverse function of either f(x) or h(x).

Giz

EDIT:  Yes, I was completely wrong!  B is correct.  They are equations of lines that are reflected about the line y=x.