Which domain restriction will allow you to find an inverse of the function f(x) = |x − 7|?
a. x ≥ 7
b. x ≥ 0
c. x ≥ -7
d. x > 7

Step-by-step explanation:

If you graph  f(x) = |x − 7| you will see a 'v'-shaped graph with vertex at (0, 0).

Try drawing a horiz. line thru this graph; it will intersect the graph in more than one place.  Thus, this function fails the "horiz. line test."

If you restrict the domain of  f(x) = |x − 7|  to [7, ∞), you'll find that that same horiz. line will intersect the graph only once.  This indicates the existence of an inverse function of f(x) = |x − 7| for this limited domain.

The correct option is B. x ≥ 0

Step-by-step explanation:

The function f(x) is given to be :

f(x) = |x - 7|

So, The function is an absolute value or mod function

And the absolute value function always gives the absolute value of the function and always gives a value greater than or equal to 0

So, f(x) ≥ 0

⇒ |x - 7| ≥ 0

So, to find the restricted domain : find the inverse of f(x)

⇒ y = x - 7

Interchange x and y

⇒ x = y - 7

⇒ y = x + 7

So, x ≥ 0

Therefore, To find an inverse the restricted domain would be x ≥ 0

Thus, The correct option is B. x ≥ 0