Question

Pam finds the inverse of some linear functions. She notices a pattern when doing so. She makes the followingclaim:For any linear function y = cx + d such that y is a function of X, c40, and duo, its inverse function can beexpressed as y=-x-d.Part ADetermine a linear function in the form y = cx + d that supports Pam's claim, Enter your answer in the firstresponse boxParteDetermine a linear function in the form y = cx + d that refutes Pam's claim. Enter your answer in the secondresponse box

Answer 1

Step 1

Part A

Let us consider the equation y = x +5 in the form of y = cx + d, which supports Pam's claims

Where

c = 1

And

d= 5

Then according to Pam, the inverse is given by

`\begin{gathered} y=(1)/(1)x-5=x-5 \\ y=x-5 \end{gathered}`

Step 2

Find the inverse of the function in step 1

`\begin{gathered} x\text{ = y -5} \\ so\text{ that } \\ \text{replacing x with y and vice versa} \\ y\text{ = }(1)/(1)x\text{ -5} \\ y\text{ = x-5} \end{gathered}`

Hence the function y = x-5 supports Pam's claim

Step 3

Part B

Let us consider the equation y = 2x + 3 in the form of y = cx + d, which supports Pam's claims

Where

c = 2

And

d= 3

Then according to Pam, the inverse is given by

`\begin{gathered} y=(1)/(2)x-3 \\ y=(1)/(2)x-3 \end{gathered}`

Step 4

Find the inverse of the function in step 3

`\begin{gathered} 2x=y-3 \\ so\text{ that } \\ \text{replacing x with y and vice versa} \\ y\text{ = }(1)/(2)x\text{ -}(3)/(2) \\ y=(1)/(2)x-(3)/(2) \end{gathered}`

Hence the function is different from the one we got in Pam's claim, hence it does not support it.