SOLUTION: 1). If f(x) =2x2+1 and g(x)=x-3, find (f o g)(x). a. (f o g)(x) = 2x 2 - 17 b. (f o g)(x) = 2x 2 - 12x + 19 c. (f o g)(x) = 2x 2 - 2 d. (f o g)(x) = 2x 2 - 12x + 13 2). Is

Algebra ->  Functions -> SOLUTION: 1). If f(x) =2x2+1 and g(x)=x-3, find (f o g)(x). a. (f o g)(x) = 2x 2 - 17 b. (f o g)(x) = 2x 2 - 12x + 19 c. (f o g)(x) = 2x 2 - 2 d. (f o g)(x) = 2x 2 - 12x + 13 2). Is      Log On


   

Question 57476: 1). If f(x) =2x2+1 and g(x)=x-3, find (f o g)(x).
a. (f o g)(x) = 2x 2 - 17
b. (f o g)(x) = 2x 2 - 12x + 19
c. (f o g)(x) = 2x 2 - 2
d. (f o g)(x) = 2x 2 - 12x + 13
2). Is the graph of y=x2+5 symmetric with respect to the origin, the x-axis, the y-axis, or the line y = x?
a. the x-axis
b. the y-axis
c. the origin
d. the line y = x

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
1). If f%28x%29=2x%5E2%2B1 and g%28x%29=x-3, find (f o g)(x).
a. (f o g)(x) =2x%5E2-17
highlight%28b%29. (f o g)(x) = 2x%5E2-12x%2B19
c. (f o g)(x) = 2x%5E2-2
d. (f o g)(x) = 2x%5E2-12x%2B13
:
Here's why:
(fog)(x)=f(g(x))=f(x-3) substitute (x-3) everywhere there is an x in the f(x) function and you get:
%28fog%29%28x%29=2%28x-3%29%5E2%2B1
%28fog%29%28x%29=2%28x%5E2-6x%2B9%29%2B1
%28fog%29%28x%29=2x%5E2-12x%2B18%2B1
%28fog%29%28x%29=2x%5E2-12x%2B19 (b)
:
2). Is the graph of y=x%5E2%2B5 symmetric with respect to the origin, the x-axis, the y-axis, or the line y = x?
a. the x-axis
highlight%28b%29. the y-axis
c. the origin
d. the line y = x
:
Here's why
The rule says that if f(-x)=f(x) there is symmetry to the y-axis.
f%28x%29=x%5E2%2B5
f%28-x%29=%28-x%29%5E2%2B5=%28-x%29%28-x%29%2B5=x%5E2%2B5
Therefore f(-x)=f(x), and the graph is symmetric to the y-axis, see:
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B5%29
Happy Calculating!!!