5.1 Composite Functions Goals 1.Form f(g(x)) = (f  g) (x) 2.Show that 2 Composites are Equal.

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5.1 Composite Functions Goals 1.Form f(g(x)) = (f  g) (x) 2.Show that 2 Composites are Equal

Evaluate a Composite Function (text p. 393) (text p. 393) f (x) = 2x 2 – 3 f (x) = 2x 2 – 3 g(x) = 4x g(x) = 4x Find f 0 g (1) and g 0 g (-1)

Find a Composite Function (text p. 393) Given, f(x) = x 2 + 3x -1 g(x) = 2x + 3 Find f  g and g  f

What do you notice from the previous example? f ○ g (x) ≠ g ○ f (x) f ○ g (x) ≠ g ○ f (x)

Show that 2 composites are equal (text p. 395) Given, functions f and g such that, f(x) = 3x  4 g(x) = ⅓(x + 4) Show that f ○ g (x) = g ○ f (x) = x for every x. for every x.

SOLUTION (f  g) (x) = f(g(x)) = f( ⅓( x + 4 ) ) = f( ⅓( x + 4 ) ) = 3( ⅓(x + 4 ) ) - 4 = 3( ⅓(x + 4 ) ) - 4 = x + 4 – 4 = x + 4 – 4 = x = x

(g  f) (x) = g(f(x)) = g( 3 x + 4 ) = g( 3 x + 4 ) = ⅓ [(3x - 4 )+ 4 ] = ⅓ [(3x - 4 )+ 4 ] = ⅓ (3x) = ⅓ (3x) = x = x

When f(g(x)) = g (f (x)) We say that the functions are INVERSE OF EACH OTHER

5.2 Inverse Functions Goals 1.Determine the Inverse of a Function 2.Obtain the Graph of the Inverse from a given Graph 3.Find f -1 the inverse function

Example 1 (text p. 400) Example 2 (text p. 401)

Discussion of example 5 text p. 405 Finding the Inverse Function text p. 407

In groups 1. # 51p # 23 p # 9 item c p # 47p. 398