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1. Solve: 7^3x-4=492. Let f(x)=x^2+10×40
-find vertex
-state the range of the function
-on what interval is the function increasing?3. Multiply and Simplify (7+6i)(2+9i)
Write the answer in the form a+bi, where a and b are real numbers.1. Solve: 7^3x-4=49Solution. As 49=7^2, 7^3x-4=49 <==> 7^3x-4=7^2.
So, 3x-4=2
i.e., 3x=6
So, x=6/3=22. Let f(x)=x^2+10x 40
– find vertex
– state the range of the function
– on what interval is the function increasing?Solution: ******** I assume that f(x)=x^2+10x +40 *******We can rewrite f(x) as f(x)=(x+5)^2+15
So,
(1) the vertex of the parabola is (-5, 15);
(2) As f(x)>=15, the range of f(x) is [15, infinity)
(3) As the parabola is open upward, the function is increasing on [-5, infinity)3. Multiply and Simplify (7+6i)(2+9i)
Write the answer in the form a+bi, where a and b are real numbers.Solution. Using the fact that i^2=-1, we have
(7+6i)(2+9i) =7*(2+9i) +(6i)*(2+9i)
=[14+63i]+ [12i – 54]
=(14-54)+ (63+12)i
= -40+75i.

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