Solution Manual For Calculus Early Transcendental Functions, 8th Edition by Ron Larson, Bruce H. Edwards (Cengage Learning, 2024) ISBN: 9780357759325, All Chapters

CHAPTERa27 TRANSCENDENTALa2FUNCTIONS

7.1 INVERSEa2FUNCTIONSa2ANDa2THEIRa2DERIVATIVES

1. Yesa2one-to-one,a2thea2grapha2passesa2thea2horizontala2linea2test.

2. Nota2one-to-one,a2thea2grapha2failsa2thea2horizontala2linea2test.

3. Nota2one-to- ya2a22a 2 intersectsa2thea2grapha2twice.
onea2sincea2(fora2example)a2thea2horizontala2line

4. Nota2one-to-one,a2thea2grapha2failsa2thea2horizontala2linea2test.

5. Yesa2one-to-one,a2thea2grapha2passesa2thea2horizontala2linea2test.

6. Yesa2one-to-one,a2thea2grapha2passesa2thea2horizontala2linea2test.

7. Nota2one- ya2a23a 2 intersectsa2thea2grapha2ana2infinitea2numbera2ofa2times.
toa2onea2sincea2thea2horizontala2line

8. Yesa2one-to-one,a2thea2grapha2passesa2thea2horizontala2linea2test.

9. Yesa2one-to-one,a2thea2grapha2passesa2thea2horizontala2linea2test.

10. Nota2one- ya2a21a 2 intersectsa2thea2grapha2twice.
toa2onea2sincea2(fora2example)a2thea2horizontala2line

11. Domain:a 2 0a2a2 xa2a21,a 2 Rang 12. Domain:a 2 xa2a21,a 2 R ya2a20
e:a 2 0a2a2 y ange:




13. Domain:a 2 1a2a2xa2a21,a 2 Range:a 2 a2a 2 a2 ya2a2 14.a 2 Domain:a 2  a2 xa2a2,a 2 Range:a 2 a2a 2 a2 ya2a2 
2 2 2 2
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,430 Chaptera27a2Transcendentala2Functions

15.a 2 Domain:a 2 0a2a2 xa2a26,a 2 Range:a 2 0a2a 2 ya2a23 16.a 2 Domain:a 2 2a2a2 xa2a21,a 2 Range:a 2 1a2a2 ya2a23




17. Thea2grapha2isa2symmetrica2 ya2 a2 x.
about




(b) ya2 a 2 a 2 1a2x2a 2 a 2 y2a 2 a21a2x2a 2 a2 a 2 y a 2 fa21(x)
x2a 2 a21a2 y2a 2 a2 xa2  1a 2 y a2  1a2a2
2
x2
18. Thea2grapha2isa2symmetrica2 ya2 a2x.
about




ya2xa2a21a 2 ya2 xa2a2a21a 2 a 2 ya2 a2a21a 2 a 2 fa21(x)
x


19. Stepa2 ya2 a2 x2a 2 1a2a2 x2a 2 a 2 ya21a2a2 xa2 
1: ya2
xa2
Stepa22: ya 1 a 2 fa21(x) 1
2 


20. Stepa2 ya2 a2 x2a 2 a ya2,a 2 sincea 2 xa2a20.
1: 2 xa2a2
x
Stepa22: ya2 a2 a 2 fa21(x)


21. Stepa2 ya2 a2 x3a2 1a2a2 x3a 2 a 2 ya21a2a2 xa2 a2(a2ya21)1/3
1: 3a 2 xa2
Stepa22: ya 1 a 2 fa21(x)
2 


22. Stepa2 ya2 a2 x2a 2 a22xa21a2a 2 ya2 a2(xya21)2a 2  a2xa21,a 2 sinceay 2 xa2a21a2a2 xa2a21
1:
ya2 a21 x a 2 fa21(x)
Stepa22:

, 23. Stepa2 ya2 a2(xa21)2a 2y y a2 xa21,a 2 sincea 2 xa2a21a2a2 xa2 1
1: 1
ya2 x 1a2a 2 fa2 (x)
Stepa22:


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