Question

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

(a) Solve the equation: $F\left(x\right)=g\left(x\right)$.

(b) Solve the inequality:$g\left(x\right)\le f\left(x\right)<h\left(x\right)$

Short answer

Part (a) $x=-6$.

Part (b) $\left\{x|-6\le x<5\right\}$.

Step-by-step solution

Part (a) Step 1. Given information.

The given figure is as follows,

There are three lines$f\left(x\right),g\left(x\right),h\left(x\right)$.

Part (a) Step 2. Explanation.

The equation $f\left(x\right)=g\left(x\right)$represent the intersection of graph role="math" localid="1647231491427" $f\left(x\right)$and $g\left(x\right)$.

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

Hence solution of$f\left(x\right)=g\left(x\right)$is$x=-6$.

Part (b) Step 1. Explanation.

The points $\left(0,12\right),\left(5,12\right)$are on $h\left(x\right)$.

The points $\left(-6,-5\right),\left(0,-5\right)$are on $g\left(x\right)$.

The points $\left(5,12\right),\left(-6,-5\right)$are on $f\left(x\right)$.

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 $g\left(x\right)$at $\left(-6,-5\right)$.

For $g\left(x\right)\le f\left(x\right)<h\left(x\right)$, here lower value of x is -6 and upper value is 5.

So solution of inequality is$\left\{x|-6\le x<5\right\}$.