SECTION 2.1 Functions 67 (d) Substitute −x for x in the equation for f and simplify. ( ) ( ) ( ) − = − − − = + f x x x x x 2 3 2 3 2 2 Notice the use of parentheses here. (e) ( ) ( ) − = − − = − + f x x x x x 2 3 2 3 2 2 (f) Substitute x3 for x in the equation for f and simplify. ( ) ( ) = − ⋅ = ⋅ − = − f x x x x x x x 3 2 3 3 3 2 9 9 18 9 2 2 2 (g) Substitute +x 3 for x in the equation for f and simplify. ( ) ( ) ( ) ( ) + = + − + = + + − − = + + − − = + + f x x x x x x x x x x x 3 2 3 3 3 2 6 9 3 9 2 12 18 3 9 2 9 9 2 2 2 2 (h) Substitute +x h for x in the equation for f and simplify. ( ) ( ) ( ) ( ) + = + − + = + + − − = + + − − f x h x h x h x xh h x h x xh h x h 2 3 2 2 3 3 2 4 2 3 3 2 2 2 2 2 Notice in this example that ( ) ( ) ( ) ( ) ( ) + ≠ + − ≠ − f x f x f f x f x 3 3 , , and ( ) ( ) ≠ f x f x 3 3 . Now Work PROBLEM 43 Most calculators have special keys that allow you to find the value of certain commonly used functions. Examples are keys for the square function ( ) = f x x ,2 the square root function ( ) = f x x, and the reciprocal function ( ) = = − f x x x 1 .1 COMMENT Graphing calculators can be used to evaluate a function. Figure 15 shows the function ( ) = = − Y f x x x 2 3 1 2 evaluated at 3 on a TI-84 Plus CE graphing calculator and on Desmos. Figure 15 Evaluating ( ) = − f x x x 2 3 2 for = x 3 Finding Values of a Function on a Calculator Verify the following results on your calculator. (a) ( ) ( ) = = = f x x f 1.234 1.234 1.522756 2 2 (b) ( ) ( ) = = ≈ F x x F 1 1.234 1 1.234 0.8103727715 (c) ( ) ( ) = = ≈ g x x g 1.234 1.234 1.110855526 EXAMPLE 7 Need to Review? Squaring a binomial such as ( ) +x 3 2 is discussed in Appendix A, Section A.3, p. 25. ■
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