Questions: If f(x) = 4/3 x + 4 and g(x) = 3^z + 1, find all values of x, to the nearest tenth f(x) = g(x).

Transcript text: If $f(x)=\frac{4}{3} x+4$ and $g(x)=3^{z}+1$, find all values of $x$, to the nearest tenth $f(x)=g(x)$.

Solution

Solution Steps

Step 1: Identify the intersection points

The problem asks for the values of $x$ where $f(x) = g(x)$. Graphically, this corresponds to the points where the graphs of $y=f(x)$ and $y=g(x)$ intersect. Looking at the graph, we can see two intersection points.

Step 2: Estimate the first intersection point

The first intersection point lies close to $x=-3$. We can see that the line representing $f(x)$ goes through the point $(-3, 0)$ and the exponential curve representing $g(x)$ appears to pass very close to that point as well. Thus, our first approximate solution is $x \approx -3$.

Step 3: Estimate the second intersection point

The second intersection point appears to be between $x=0$ and $x=1$. Looking closely, we can estimate the $x$ value to be near $0.7$ or $0.8$. Since we are asked to approximate to the nearest tenth, we can visually estimate $x \approx 0.7$.