Q. 31 - Precalculus Enhanced with Graphing Utilities

Question

In parts (a) – (f), use the following figure. 

(a) Solve $f\left(x\right)=50$                        (b) Solve $f\left(x\right)=80$

(c) Solve $f\left(x\right)=0$                          (d) Solve $f\left(x\right)>50$

(e) Solve $f\left(x\right)\le 80$                        (f) Solve $0<f\left(x\right)<80$

Step-by-Step Solution

Answer

Part (a) $x=40$

Part (b)  $x=88$

Part (c)  $x=-40$

Part (d) $\left\{x|x>40\right\}$

Part (e) $\left\{x|x\le 88\right\}$

Part (f) $\left\{x|-40<x<88\right\}$

Part (a). Step 1 Given information

The graph is given 

Answer the question using the graph.

Part (a) Step 2. Explanation

To solve $f\left(x\right)=50$

We know that, $f\left(x\right)=y$ so, $y=50$

As here $y=50$ from graph we can find corresponding value of x. 

So, we have point $\left(40,50\right)$in on the given graph. So, $x=40$

So, $f\left(x\right)=50$when $x=40$

Part (b) Step 1. Explanation

To solve $f\left(x\right)=80$

We know that, $f\left(x\right)=y$ so, $y=80$

As here $y=80$ from graph we can find corresponding value of x. 

So, we have point $\left(88,80\right)$ in on the given graph. So, $x=80$

So, $f\left(x\right)=80$ when $x=88$

Part (c) Step 1. Explanation

To solve $f\left(x\right)=0$

We know that, $f\left(x\right)=y$  so, $y=0$

As here $y=0$ from graph we can find corresponding value of x.

 

So, we have point $\left(-40,0\right)$ in on the given graph. So, $x=-40$

So,  $x=-40$ when $f\left(x\right)=0$

Part (d) Step 1. Explanation

To solve $f\left(x\right)>50$

We know that, $f\left(x\right)=y$ 

As here $y>50$ from graph we can find corresponding value of x.

So, we have point $\left(40,50\right)$ in on the given graph.

So, for $y>50$ $\Rightarrow x>40$.

Part (e) Step 1. Explanation

To solve $f\left(x\right)\le 80$

We know that, $y=f\left(x\right)$ so, $y=80$

From graph we can find corresponding value of x. 

So, we have point $\left(88,80\right)$ in on the given graph. So, $x=88$ 

For  $y\le 80\Rightarrow x\le 88$

Part (f) Step 1. Explanation

To solve $0<f\left(x\right)<80$

We know that, $f\left(x\right)=y$ so, $0<y<80$

We can find corresponding value of x. 

So, we have points $\left(-40,0\right)$ and $\left(88,80\right)$ in on the given graph.

So, $0<y<80\Rightarrow -40<x<88$