Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer 2

Answer:

The correct option is D.

Step-by-step 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: $\frac{x-5}{7}=y$

Reason: Divide each side by 7.

Step 6: $\frac{x-5}{7}=g(x)$

Reason: Change y to g(x).

Step 7: $g(x)=\frac{x-5}{7}$

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.