Question

Find the inverse of g(x)=x-2/5. What does this tell you about the relationship between f(x)=5x+2 and g(x)?

Answer 1

Given a function as shown below:

`g(x)\text{ = }(x-2)/(5)`
`\begin{gathered} g(x)=(x-2)/(5) \\ \text{Inverse of g(x) = g}^(-1)(x) \\ \text{cross multiply } \\ \text{5g(x) = x-2} \\ 5g(x)+2\text{ = x} \\ x=5g(x)+2 \end{gathered}`
`g^(-1)(x)=5x+2`

Since the function of f(x) = 5x+2 and also inverse of g(x) = 5x+2

Therefore from the observation, the inverse of g(x) is similar to the function of f(x)

Hence the function of f(x) = inverse of g(x)