Mac2311Q1A

# Mac2311Q1A - θ = √ 1 x 2 Hence cos arctan x = cos θ = 1 sec θ = 1 √ 1 x 2 Instead of using trignometric identities like I have done(ugh you

This preview shows pages 1–2. Sign up to view the full content.

Solutions to MAC 2311 Quiz 1 A Jason Harrington January 28, 2006 1. (1 pt) Determine whether the statement is TRUE or FALSE: ”The domain of f - 1 = domain of f This statement above is false. The true statement should read: ”The domain of f - 1 = range of f 2. (3 pts) Let f ( x ) = ln( x ), write the equation of the graph that results from (a) shifting down 2 units y = ln( x ) - 2 (b) reﬂecting about the x-axis y = - ln( x ) (c) shifting 2 units to the left y = ln( x + 2) 3. (2 pts) Find the inverse for the following function: f ( x ) = 3 1 - 2 x x = 3 1 - 2 y x 3 = 1 - 2 y x 3 - 1 = - 2 y 1 - x 3 = 2 y ln(1 - x 3 ) = ln(2 y ) ln(1 - x 3 ) = y ln(2) ln(1 - x 3 ) ln(2) = y Therefore: f - 1 ( x ) = ln(1 - x 3 ) ln(2) 4. (2 pts) Simplify the expression: cos(arctan x ) Let θ = arctan( x ). Now recall that - π 2 < θ < π 2 Now, recall that sec 2 ( θ ) = 1 + tan 2 ( θ ) = 1 + x 2 . Thus sec(

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: θ ) = √ 1 + x 2 . Hence, cos arctan( x ) = cos( θ ) = 1 sec( θ ) = 1 √ 1+ x 2 Instead of using trignometric identities like I have done (ugh. ..) you may try to ﬁnd this solution by using a diagram (sigh of relief). 1 5. (2 pts) Find the domain (in interval notation) for the following functions: (a) f ( x ) = e x 1+ e x Since 1 + e x 6 = 0 for all x , the domain is the whole real line. Or (-∞ , ∞ ) (b) g ( t ) = √ 1-3 t We cannot take the square root of a negative number i.e., 1-3 t ≥ so. .. 1-3 t ≥ 1 ≥ 3 t ln(1) ≥ ln(3 t ) ≥ t ln(3) ≥ t Thus, the doman is (-∞ , 0] 2...
View Full Document

## This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

### Page1 / 2

Mac2311Q1A - θ = √ 1 x 2 Hence cos arctan x = cos θ = 1 sec θ = 1 √ 1 x 2 Instead of using trignometric identities like I have done(ugh you

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online