Question

Give the equation of any asymptote for the graph f(x). Then write the equation for g(x)(The function g(x) is the inverse of f(x))

Answer 1

(a)x=0

(b)g(x)=5^x

Explanation:

Given the function:

`f(x)=\log_5x`

(a)The vertical asymptote for the graph of f(x) is:

`x=0`

(b)Next, we find the equation for g(x), the inverse of f(x).

`\begin{gathered} f(x)=\log_5x \\ \implies y=\log_5x \end{gathered}`

Swap x and y:

`x=\log_5y`

Then solve for y:

`\begin{gathered} y=5^x \\ \implies f^(-1)(x)=5^x \\ \implies g(x)=5^x \end{gathered}`

The equation for g(x) is:

`g(x)=5^x`