a. Show that h(x) = x3/4 and k(x) = (4x)^(1/3) are inverses of one another. b. Graph h and k over an x-interval large enough to show the graphs intersecting at (2, 2) and (-2, -2). Be sure the picture shows the required symmetry about the line y = x. c. Find the slopes of the tangents to the graphs at h and k at (2, 2) and (-2, -2). d. What lines are tangent to the curves at the origin
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
a. Show that h(x) = x3/4 and k(x) = (4x)^(1/3) are inverses of one another.
b. Graph h and k over an x-interval large enough to show the graphs intersecting at (2, 2) and (-2, -2). Be sure the picture shows the required symmetry about the line y = x.
c. Find the slopes of the tangents to the graphs at h and k at (2, 2) and (-2, -2).
d. What lines are tangent to the curves at the origin
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