Question

A function and its inverse are shown on the same graph.

f(x)
x
6.
Which statement describes the relationship between the
function and its inverse?
O The slope of f¹(x) is the same as the slope of f(x).
The slope of f¹(x) is the opposite as the slope of f(x).
O The x-intercept of f¹(x) is the same as the y-intercep
of f(x).
The x-intercept of f¹(x) is the opposite as the y-
intercept of f(x).

Answer 1

(c) The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

Inverse function

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

f⁻¹(b) = a

Application

If an ordered pair (x-intercept) of the inverse function is ...

(P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

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Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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