# Operations with Functions

1. Solve: 7^3x-4=49

2. Let f(x)=x^2+10x40

-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.

https://brainmass.com/math/algebra/operations-functions-518729

## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. Solve: 7^3x-4=49

Solution. 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=2

2. 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.

https://brainmass.com/math/algebra/operations-functions-518729