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Chapter 3: Q. 36 (page 137)

In parts (a) and (b), use the following figure.

(a) Solve the equation: f(x)=g(x).

(b) Solve the inequality:g(x)<f(x)鈮�h(x)

Short Answer

Expert verified

Part (a) x=7.

Part (b)x|-4<x鈮�7.

Step by step solution

01

Part (a) Step 1. Given information. 

The given figure is as follows,

There are three linesf(x),g(x),h(x).

02

Part (a) Step 2. Explanation. 

The equation f(x)=g(x)represent the intersection of graph f(x)and g(x).

Here intersection of graph f(x),g(x)is 7,-8, the value of x is 7.

Hence, solution of f(x)=g(x)isx=7.

03

Part (b) Step 1. Explanation.

The points -4,7,0,7 are on h(x).

The points 0,-8,7,-8are on g(x).

The points -4,7,7,-8are on f(x).

The values of h(x)are greater than values of function g(x).

The function f(x) is intersecting h(x) at -4,7 and g(x)at 7,-8.

For gx<fx鈮�hx, here lower value of x is -4 and upper value is 7.

So solution of inequality is x|-4<x鈮�7.

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