Question

Part CHow can the equation 3* = 4x + 1 be used to check any solutions indicated by the graphs of y = f(x) andy = g(x)?

Answer 1

See explanation below

Step-by-step explanation:

The solution sets of the y = f(x) and y = g(x) are gotten from their point of intersections.

f(x) = 3^x, g(x) = 4x + 1

From th graph, they intersect at points (0, 1) and (2, 9).

They are solutions to each of the fu

To use th 3^x = 4x + 1 to determine if the solution set is correct, we can input the value of x into this equation.

If it is a solution, then the left hand side of the of the equation will be equal to the right hand side

Now, let's test if points (0, 1) and (2, 9) are solutions of y = 3^x and y= 4x + 1 using 3^x = 4x + 1:

when x = 0

`\begin{gathered} 3^x=4x+1 \\ 3^0\text{ = 4(0) + 1} \\ 1\text{ = 0 + 1} \\ 1\text{ = 1 (left hand side = right hand side)} \end{gathered}`
`\begin{gathered} \text{when x = 2} \\ 3^x=4x+1 \\ 3^2\text{ = 4(2) + 1} \\ 9\text{ = 8 + 1} \\ 9\text{ = 9 (left hand side = right hand side)} \end{gathered}`

This indicates that the solution of y = f(x) and y = g(x) will be the same as when both functions are equated (3^x = 4x + 1)