Let L1(x) = mx + b where m doesn't equal 0. Let L2(x) be the inverse function of L1(x).?

Posted on 2015-10-30 12:34:00 in Math by KYLER

Let L1(x) = mx + b where m doesn't equal 0. Let L2(x) be the inverse function of L1(x).

(a) Find L2(x).

(b) If m doesn't equal 1, ?1, then show that the graphs of L1(x) and L2(x) intersect at the point
(?b/(m ? 1),?b/(m ? 1))

Suppose that f(x) is a differentiable function and assume that g(x) is the inverse
function of f(x). Let L1(x) be the linearization of f(x) at x = a and let L2(x) be the
linearization of g(x) at x = b where b = f(a). In the following problems, use the results of Problem 1

(a) Write the formulas for L1(x) and L2(x).

(b) How are the slopes of L1(x) and L2(x) related?

(c) If the graph of L1(x) is not a horizontal line, then show that L2(x) is the inverse function
of L1(x). (It is helpful to use that b = f(a) and a = g(b) in this problem.)

(d) If f'(a) doesn't equal ±1, explain why the graphs of L1(x) and L2(x) intersect on the line given by y= x

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