Question

select the correct answer.
keith used the following steps to find the inverse of f, but he thinks he made an error.

step 1 $f(x) = 7x + 5$ given
step 2 $y = 7x + 5$ change f(x) to y
step 3 $x = 7y + 5$ switch x and y
step 4 $x + 5 = 7y$ add 5 to each side
step 5 $\frac{x+5}{7} = y$ divide each side by 7
step 6 $\frac{x+5}{7} = g(x)$ change y to g(x)
step 7 $g(x) = \frac{x+5}{7}$ switch sides of the equation

what mistake, if any, did keith make?
a. in step 5, keith should have multiplied each side of the equation by 7
b. in step 4, keith should have subtracted 5 from each side
c. keith did not make any error
d.

Explanation:

Step1: Recall inverse function steps

To find an inverse, after switching $x$ and $y$ to get $x=7y+5$, we isolate $y$ by first undoing the $+5$.

Step2: Analyze Step 4 error

Instead of adding 5, we subtract 5 from both sides:
$x - 5 = 7y$
Keith incorrectly added 5 instead of subtracting 5 in Step 4.

Answer:

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