Question

Keith used the following steps to find the inverse off, but he thinks he made an error

A. In step 5. Keith should have multiplied each side of the equation by 7.

B. In step 6, Keith should have switched x and y

C. Keith did not make any errors.

D. In step 4 Keith should have subtracted 5 from each side.

Answer 1

The correct option is D.

Explanation:

It is given that Keith used the following steps to find the inverse off, but he thinks he made an error.

The correct steps are:

Step 1:
`f(x)=7x+5`

Reason: Given

Step 2:
`y=7x+5`

Reason: Change f(x) to y.

Step 3:
`x=7y+5`

Reason: Switch x and y.

Step 4:
`x-5=7y`

Reason: Subtract 5 from each side.

Step 5:
`(x-5)/(7)=y`

Reason: Divide each side by 7.

Step 6:
`(x-5)/(7)=g(x)`

Reason: Change y to g(x).

Step 7:
`g(x)=(x-5)/(7)`

Reason: Switch sides of the equation.

In step 4 Keith add 5 but she should have subtracted 5 from each side.

Therefore the correct option is D.

Answer 2

Option D In step 4 Keith should have subtracted 5 from each side

Explanation:

step 1

we have

f(x)=7x+5 -----> given

step 1 is correct

step 2

Change f(x) to y

y=7x+5

so

step 2 is correct

step 3

Exchange x for y and y for x

x=7y+5

so

step 3 is correct

step 4

Subtract 5 each side

x-5=7y+5-5

x-5=7y

step 4 is not correct

step 5

Divide by 7 each side

(x-5)/7=y

step 6

Change y to g(x)

(x-5)/7=g(x)

step 7

switch sides of the equation

g(x)=(x-5)/7

therefore

In step 4 Keith should have subtracted 5 from each side