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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))

Give the equation of any asymptote for the graph f(x). Then write the equation for-example-1
Give the equation of any asymptote for the graph f(x). Then write the equation for-example-1
Give the equation of any asymptote for the graph f(x). Then write the equation for-example-2

1 Answer

1 vote

Answer:

(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

User Tshilidzi Mudau
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