SOLUTION: 1. f(x)=8+x, g(x)=x-5, If d(x)=f(x)-g(x), find d(x) 2. Solve: x^2 + 6x + 6 = 0 3. f(x) = e^2x What is f(1/4)? Thank you so much!!!!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 1. f(x)=8+x, g(x)=x-5, If d(x)=f(x)-g(x), find d(x) 2. Solve: x^2 + 6x + 6 = 0 3. f(x) = e^2x What is f(1/4)? Thank you so much!!!!       Log On


   

Question 257532: 1. f(x)=8+x, g(x)=x-5, If d(x)=f(x)-g(x), find d(x)
2. Solve:
x^2 + 6x + 6 = 0
3. f(x) = e^2x
What is f(1/4)?
Thank you so much!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1. d%28x%29=f%28x%29-g%28x%29=%288%2Bx%29-%28x-5%29=8%2Bx-x%2B5=13.

So d%28x%29=13
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2.



x%5E2%2B6x%2B6=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=6


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%286%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=6


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%286%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-24+%29%29%2F%282%281%29%29 Multiply 4%281%29%286%29 to get 24


x+=+%28-6+%2B-+sqrt%28+12+%29%29%2F%282%281%29%29 Subtract 24 from 36 to get 12


x+=+%28-6+%2B-+sqrt%28+12+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%282%29+%2B-+%282%2Asqrt%283%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+sqrt%283%29 Reduce.


x+=+-3%2Bsqrt%283%29 or x+=+-3-sqrt%283%29 Break up the expression.


So the solutions are x+=+-3%2Bsqrt%283%29 or x+=+-3-sqrt%283%29


which approximate to x=-1.268 or x=-4.732

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3.


Simply plug in x=1%2F4 to get f%281%2F4%29+=+e%5E%282%281%2F4%29%29=e%5E%282%2F4%29=e%5E%281%2F2%29%5E%22%22


So f%281%2F4%29+=+e%5E%281%2F2%29%5E%22%22. In addition, you can convert to radical notation to get f%281%2F4%29+=+sqrt%28e%29