Question

Which statement identifies how to show that j(x) = 11.6ex and k(x) = In (StartFraction x Over 11.6 EndFraction) are inverse functions?

Answer 1

C

Explanation:

Ed2021

Answer 2

The answer is "It must be shown that both
`j(k(x))\ and \ k(j(x))=x`"

Step-by-step explanation:

Given:

`j(x) = 11.6 e^(x) \\\\k(x) =\ln(x)/(11.6)`

To show that both are equal functions, and show that both
`j(k(x))\ and\ k(j(x)) =x,`

For
`j(k(x));`

`j(k(x)) = j[(\ln (x)/(11.6))]\\\\j[(\ln ((x)/(11.6))] = 11.6e^{\ln ((x)/(11.6))}\\\\j[(\ln (x)/(11.6))] = 11.6((x)/(11.6))\\\\`(The natural logarithm is canceled by exponential function)

`j[(\ln (x)/(11.6))] = 11.6 *(x)/(11.6)\\\\j[(\ln (x)/(11.6))] = x\\\\j[k(x)] = x\\\\for\ \ k[j(x)]:\\\\k[j(x)] = k[11.6e^x]\\\\k[11.6e^x] = \ln ((11.6e^x)/(11.6))\\\\k[11.6e^x] = \ln(e^x)`

Its natural logarithm leaving x will nullify expanding universe.

`k[11.6e^x] = x\\\\k[j(x)] = x`

In the question, it is seen that
`j[k(x)] = k[j(x)] = x`, shows that the functions
`j(x) = 11.6 e^(x) \ and \ k(x) = \ln (x)/(11.6)` is inverse functions.