and f-[{1,3}] = {a, b, c, d}. 1.5. IMAGES AND INVERSES X a b Let f...

 

 

Transcribed Image Text:

and f-¹[{1,3}] = {a, b, c, d}. 1.5. IMAGES AND INVERSES X a b Let f be as in Figure 1.33 Then f[{b,c}] = {1,3} C e Y 2 3 4 FIGURE 1.33. Picture of f 33 a) What is the range of f? b) is fonto? Explain your answer. c) Is f 1-to-1? Explain your answer. 2. Consider the function g(x) = x³ on the real numbers. Is g(x) 1-to-1? Is g(x) onto? For positive answers, you can give formal proof or argue from the function graph. For negative answers, a counterexample is enough. 3. Consider the function h(x) = x² on the real numbers. Is h(x) 1-to-1? Is h(x) onto? and f-¹[{1,3}] = {a, b, c, d}. 1.5. IMAGES AND INVERSES X a b Let f be as in Figure 1.33 Then f[{b,c}] = {1,3} C e Y 2 3 4 FIGURE 1.33. Picture of f 33 a) What is the range of f? b) is fonto? Explain your answer. c) Is f 1-to-1? Explain your answer. 2. Consider the function g(x) = x³ on the real numbers. Is g(x) 1-to-1? Is g(x) onto? For positive answers, you can give formal proof or argue from the function graph. For negative answers, a counterexample is enough. 3. Consider the function h(x) = x² on the real numbers. Is h(x) 1-to-1? Is h(x) onto?