Question

How do I do this question?​

Answer 1

Choice C

Explanation:

We are given the function:

`\displaystyle \large{f(x)=3x+5}`

Let
`\displaystyle \large{y=f(x)}` therefore:

`\displaystyle \large{y=3x+5}`

To find an inverse of function, swap the position of x and y:

`\displaystyle \large{x=3y+5}`

Then solve or simplify the equation in term of y:

`\displaystyle \large{x-5=3y}\\\displaystyle \large{(x-5)/(3)=y}\\\displaystyle \large{y=(1)/(3)x-(5)/(3)}`

Therefore, the answer is choice C.

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Summary

An inverse function is a function that swaps the position of domain and range, defined as notation
`\displaystyle \large{f^(-1)(x)}` or
`\displaystyle \large{y^(-1)}` generally. When finding an inverse function, make sure to swap position of range and domain, if given the interval.

Only one-to-one functions may have an inverse — multiple-to-one can not have an inverse such as quadratic function or any even-degree polynomial functions.

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Others

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