a.) Sketch the graph of f
b.) Show that the function f(x)=1+4√x is one to one.
c.) Use part(a) to sketch the graph of f−1
d.) Find an equation of f−1
a.)
b.) It shows from the graph of f that the function is a one to one function since there is only one corresponding y-value for each value of x. Also, if you use Horizontal Line Test, the line will intersect the function only once.
c.) To sketch the graph of f−1 we reflect the graph of f about the line y=x
d.) To find the equation of f−1, we set y=f(x)
y=1+4√xSolve for x, subtract 14√x=y−1Raise both sides by 4x=(y−1)4Interchange x and yy=(x−1)4
Thus, f−1(x)=(x−1)4 for x>1
Wednesday, November 2, 2016
College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 92
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