Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. A function could have the property that ƒ1-x2= ƒ1x2, for all x. b. cos1a + b2= cos a + cos b, for all a and b in 30, 2p4. c. If ƒ is a linear function of the form ƒ1x2= mx + b, then ƒ1u + v2= ƒ1u2+ ƒ1v2, for all u and v. d. The function ƒ1x2= 1 - x has the property that ƒ1ƒ1x22= x. e. The set 5x: | x + 3| 7 46 can be drawn on the number line without lifting your pencil. f. log101xy2=1log10 x21log10 y2. g. sin-11sin 2p2= 0.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. A function could have the property that ƒ1-x2= ƒ1x2, for all x.
b. cos1a + b2= cos a + cos b, for all a and b in 30, 2p4.
c. If ƒ is a linear function of the form ƒ1x2= mx + b, then ƒ1u + v2= ƒ1u2+ ƒ1v2, for all u and v.
d. The function ƒ1x2= 1 - x has the property that ƒ1ƒ1x22= x.
e. The set 5x: | x + 3| 7 46 can be drawn on the number line without lifting your pencil.
f. log101xy2=1log10 x21log10 y2.
g. sin-11sin 2p2= 0.
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