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I need some help on question 4 I would appreciate it:0

I need some help on question 4 I would appreciate it:0-example-1
User Peter Nied
by
8.2k points

1 Answer

5 votes


c)f^(-1)(x)=-(x)/(5)-(8)/(5)

Step-by-step explanation
f(x)=-8-5x

An inverse function essentially undoes the effects of the original function,it is given by


f^(-1)(x)\rightarrow inverse\text{ of f(x)}

to find the inverse of a function do:

Step 1

strick a "y" in f(x)


\begin{gathered} f(x)=-8-5x \\ y=-8-5x \end{gathered}

Step 2

swap x and y


\begin{gathered} y=-8-5x \\ y=-8-5x\rightarrow x=-8-5y \\ x=-8-5y \end{gathered}

Step 3

solve for y and write in the inverse notation


\begin{gathered} x=-8-5y \\ \text{add 8 in both sides} \\ x+8=-8-5y+8 \\ x+8=-5y \\ \text{divide both sides by -5} \\ (x+8)/(-5)=(-5y)/(-5) \\ -(x)/(5)-(8)/(5)=y \\ y=-(x)/(5)-(8)/(5) \end{gathered}

use the inverse notation


\begin{gathered} y=-(x)/(5)-(8)/(5) \\ f^(-1)(x)=-(x)/(5)-(8)/(5) \end{gathered}

so, the answer is


c)f^(-1)(x)=-(x)/(5)-(8)/(5)

I hope this helps you

User Jst
by
8.8k points

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