Question

Which point is on the graph of the inverse function h–1(x)?

Answer 1

The points in the inverse h⁻¹(x) are:

(6, -2), (2, 0), (-2, 2), (-6, 4)

Which point is on the graph of the inverse function h⁻¹(x)?

Remember that the inverse of a function f(x) is defined as follows:

if f(x)= y

then f⁻¹(y) = x

So if (x, y) is in the graph of f, then (y, x) is on the graph of f⁻¹(x)

Now, in the graph of h(x) we can see that it passes through the passes through the points:

(-2, 6), (0, 2), (2, -2), (4, -6)

Then the points in the inverse are:

(6, -2), (2, 0), (-2, 2), (-6, 4)

Answer 2

Given:

The graph of the function h(x)

Picking any point on the graph as shown below,

Picking point (0,2) on the graph of the function h(x)

`\begin{gathered} x=0 \\ y=2 \\ \\ \text{Hence, the point of the inverse function is gotten by interchanging the coordinates of the point } \\ ^{}^{} \end{gathered}`
`\begin{gathered} \text{If the point of h(x) is }(x,y),thenh^(-1)(x)\text{ is (y,x)} \\ \\ \text{Hence, at (0,2) on h(x)}, \\ h^(-1)(x)\text{ will have the point (2,0)} \\ \\ \text{Also, at (1,0) on h(x),} \\ h^(-1)(x)\text{ will have the point (0,1)} \end{gathered}`

Therefore, a point on the graph of the inverse function of h(x) is (2,0).

Another point on the graph of the inverse function of h(x) is (0,1).