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Chapter 3: Q. 31 (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)<h(x)

Short Answer

Expert verified

Part (a) x=-6.

Part (b) x|-6≤x<5.

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 role="math" localid="1647231491427" f(x)and g(x).

Here intersection of graph f(x),g(x)is -6,-5, the value of x is -6.

Hence solution off(x)=g(x)isx=-6.

03

Part (b) Step 1. Explanation.

The points 0,12,5,12are on h(x).

The points -6,-5,0,-5are on g(x).

The points 5,12,-6,-5are on f(x).

For all values of x, function h(x) is greater than g(x).

The function f(x) is intersecting h(x) at (5,12)and g(x)at -6,-5.

For gx≤fx<hx, here lower value of x is -6 and upper value is 5.

So solution of inequality isx|-6≤x<5.

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