# Algebra - Inverses, Domains and Composition of Functions

Use a calculator (standard scientific calculator or an online graphing calculator) to find each of the following numerical values. Write your answer rounded to 2 decimal places (i.e., the nearest hundredth).

(a) 4 -1.2

(b) e 5.76

Use composition of functions to show that the functions f(x) = 5x - 2 and are inverse functions. That is, show that and show that .

Suppose y varies inversely as x and y = 0.3 when x = 10

(a) Find the variation constant and an equation of variation.

(b) Use your results from (a) to help find y when .

Let
(a) Find the inverse function of f. Show work.

(b) State the domain of f. State the domain of the inverse function.

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#### Solution Preview

...f((x + 2)/5) = 5(x + 2)/5 - 2 = x
gof(x) = g(f(x)) = g(5x - 2) = {(5x - 2) + 2}/5 = x

Suppose y varies inversely as x and y = 0.3 when x = 10

(a) Find the variation constant and an equation of variation.
(b) Use your results from (a) to help find y when .

(a) y = k/x
k = yx = 0.3 * 10 = 3
y = 3/x
(b) y = 3/(1/2) = 6

Let
(a) Find the inverse function of f. Show work.

(b) State the ...