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Chapter 7: Q. 7 (page 505)

Sketch a graph of each of the following functions. Label at least three points on each graph. Name the inverse function of each and show its graph.

a)y=x3b)y=exc)y=sinx-蟺2鈮�x鈮�蟺2d)y=cosx0鈮�x鈮�蟺

Short Answer

Expert verified

The inverse functions can be given as

a)x=y13b)x=lnyc)x=sin-1yd)x=cos-1y

Step by step solution

01

Given information

We are given 4 functions

02

Part a) Step 1: Plot the graph

The graph of the functiony=x3 can be given as

03

Part a) Step 2: Find inverse function

We have,

y=x3takingcuberootx=y13

is the required inverse function

04

Part b) Step 1: Plot the graph

The graph of y=excan be given as

05

Part b) Step 2: Find inverse function

consider

y=exlny=x

is the required inverse function

06

Part c) Step 1: Plot the graph

The graph of function in the given domain is given as

07

Part c) Step 2: find the inverse function

The inverse function can be given as

y=sinxx=sin-1y

08

Part d) Step 1: Plot the graph of the function

The graph of the function can be given as

09

Part d) Step 2: Find the inverse function

The inverse function can be given as

y=cosxx=cos-1y

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