1. **State the problem:** We have two functions: $$f(x) = 9x + 7$$ and $$g(x) = 5^x$$ We are given some values in a table and need to complete it and find the solution to the equation $$f(x) = g(x)$$. 2. **Complete the table:** - For $$f(x)$$, calculate values for $$x=0,1,2$$: - $$f(0) = 9(0) + 7 = 7$$ - $$f(1) = 9(1) + 7 = 16$$ - $$f(2) = 9(2) + 7 = 18 + 7 = 25$$ - For $$g(x)$$, calculate values for $$x=-2,-1,2$$: - $$g(-2) = 5^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04$$ - $$g(-1) = 5^{-1} = \frac{1}{5} = 0.2$$ - $$g(2) = 5^2 = 25$$ 3. **Table completed:** | x | f(x) = 9x + 7 | g(x) = 5^x | |----|---------------|------------| | -2 | -11 | 0.04 | | -1 | -2 | 0.2 | | 0 | 7 | 1 | | 1 | 16 | 5 | | 2 | 25 | 25 | 4. **Solve the equation $$f(x) = g(x)$$:** Set $$9x + 7 = 5^x$$ This is a transcendental equation and generally solved by inspection or numerical methods. 5. **Check integer values from the table:** - At $$x=2$$, $$f(2) = 25$$ and $$g(2) = 25$$, so $$f(2) = g(2)$$. 6. **Conclusion:** The solution to $$f(x) = g(x)$$ from the given values is $$x = 2$$. **Final answer:** $$x = 2$$