Question

Given the function, ƒ(x) = (1/x+1) - 5, choose the correct transformation.

Answer 1

Answer: left 1 down 5

Explanation:

ƒ(x) = 1/x+1 - 5

The number under the 1 with the x is where you're moving on the x axis and the number after that is where you're moving on the y axis. In this case you're moving -5 from the x input and -1 (1 to the left ) from the x input

Answer 2

If we are to transform this to the inverse function, first we replace f(x) with y,
y = (1/x+1) - 5
Then, we replace all the y's with x and all the x's with y. Such that,
x = (1/y+1) - 5
Then, we solve for the value of y in terms of x in our newly generated equation.
x + 5 = 1/y+1
(x + 5)(y +1) = 1
y + 1 = 1/(x +5)
y = 1/(x + 5) - 1
So, the inverse function,
y = f⁻¹(x) = 1/(x + 5) - 1