MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C74861.F77E5DF0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C74861.F77E5DF0 Content-Location: file:///C:/213799D2/sample-2.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Test 1 Math 113

Math 123c   Sample Test 2 

 

1.  If f(x) =3D x2 + 3x,  g(x) =3D 3x – 2, h(x) =3D 3 = / (x –1), simplify the following:

A.  f( 3 ) – g( -2 )        =             &nb= sp;            =       B. (f o h)(0)

Ans: 26        =             &nb= sp;            =             &nb= sp;         Ans: 0

C.  (h o g)(x)        =             &nb= sp;            =              D. express (g o h)(x) as one fraction

Ans: 1 / (x – 1 = )        =             &nb= sp;            =         Ans: (11 – 2x) / ( x – 1 )

E.   f(x)*h(x)        =                   =             &nb= sp;       F.  f(x + h) – f(x)        =             &nb= sp;            

Ans: 3(x2 += 3x) /(x – 1)        =             &nb= sp;         Ans: h2 + 2xh + 3h

G. [g(x + a) – g= (x)] / a        =           =             &nb= sp; H. [f(x) – f(x – a )] / a

Ans: 3        =             &nb= sp;            =             &nb= sp;          Ans: 2x – a +3

 

2.  Find the domain of the following functions

        =             &nb= sp;    .


 

 

3.    Solve for the inverse formula= f-1(x) and verify that (f o f-1)(y) =3D y.

= a.      = f(x) =3D = (4x – 3) / 5        =    An= s: f -1 (x) =3D (5x + 3) / 4<= /o:p>

     b.   f(x) =3D 5 / (4x –= ;3 )        =     An= s: f -1 (x) =3D 5/(4y)  + 3/ = 4

 

4.  Find the total return of $10,000 compounded monthly at a rate =3D 12% over 15 yrs.

     Ans: 10000* 1.01= 180 =3D 59958.02

&nbs= p;

5.  a. Write  5-2 =3D 1/25= in log form        =    b. Write log 8 (2) =3D 1/3 in the exponential form 

     Ans: log 5 (1/25) =3D -2        =             &nb= sp;     Ans; 81/3 =3D 2

  &nb= sp; c.  Write  8 2/3 =3D 4  in log form            d.  Write log 4 (1/2) =3D -1= /2 in the exponential form      

     Ans: log 8<= /sub> (4) =3D 2/3        =             &nb= sp;        Ans:  4-1/2 = =3D ½

 

6.  Solve for x. No calculator.

     a.  log 6 (x) =3D=  2                =             &nb= sp;       b.  log 9 ( x) = =3D -1/2         =  

    Ans: x =3D 36        =                     =             &nb= sp; Ans: x =3D 1/3

     c.  log 3 (1/27 ) =3D x        =             &nb= sp;         d.  log x ( = 4 ) =3D  2/3        =          

  &nb= sp; Ans: x =3D -3        =             &nb= sp;            =           Ans: x =3D 8 

 

7. Give the exact answers and approximate answers to three significant digits.        =             &nb= sp; 

     a.  2* 103- x =3D 9               =               =     b.   3*LN(2x –3) =3D -5

    Ans: x =3D 3 – L= OG( 9/2)        =             &nb= sp;      Ans: x =3D (e-5/3+3)/2

      c.  12 =3D 18 – 3e3- x             =             &nb= sp;         d.  10 – 5*LOG(4 – 2x) =3D = -3

    Ans: x =3D 3= – LN(2)        =             &nb= sp;             Ans: x =3D (4 – 1013/5) / 2

        =        

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